(%i1) batch(diffeq.max) read and interpret file: /home/dennis/mastersource/mine/omnisode/diffeq.max (%i2) load(stringproc) (%o2) /usr/local/share/maxima/5.26.0/share/contrib/stringproc/stringproc.mac (%i3) display_alot(iter) := if iter >= 0 then (ind_var : array_x , omniout_float(ALWAYS, 1 "x[1] ", 33, ind_var, 20, " "), analytic_val_y : exact_soln_y1(ind_var), omniout_float(ALWAYS, "y1[1] (analytic) ", 33, analytic_val_y, 20, " "), term_no : 1, numeric_val : array_y1 , term_no abserr : abs(numeric_val - analytic_val_y), omniout_float(ALWAYS, "y1[1] (numeric) ", 33, numeric_val, abserr 100.0 20, " "), if abs(analytic_val_y) # 0.0 then relerr : ------------------- abs(analytic_val_y) else relerr : - 1.0, if glob_iter = 1 then array_1st_rel_error : relerr 1 else array_last_rel_error : relerr, omniout_float(ALWAYS, 1 "absolute error ", 4, abserr, 20, " "), omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"), omniout_float(ALWAYS, "h ", 4, glob_h, 20, " "), analytic_val_y : exact_soln_y2(ind_var), omniout_float(ALWAYS, "y2[1] (analytic) ", 33, analytic_val_y, 20, " "), term_no : 1, numeric_val : array_y2 , term_no abserr : abs(numeric_val - analytic_val_y), omniout_float(ALWAYS, "y2[1] (numeric) ", 33, numeric_val, abserr 100.0 20, " "), if abs(analytic_val_y) # 0.0 then relerr : ------------------- abs(analytic_val_y) else relerr : - 1.0, if glob_iter = 1 then array_1st_rel_error : relerr 2 else array_last_rel_error : relerr, omniout_float(ALWAYS, 2 "absolute error ", 4, abserr, 20, " "), omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"), omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ")) (%o3) display_alot(iter) := if iter >= 0 then (ind_var : array_x , omniout_float(ALWAYS, 1 "x[1] ", 33, ind_var, 20, " "), analytic_val_y : exact_soln_y1(ind_var), omniout_float(ALWAYS, "y1[1] (analytic) ", 33, analytic_val_y, 20, " "), term_no : 1, numeric_val : array_y1 , term_no abserr : abs(numeric_val - analytic_val_y), omniout_float(ALWAYS, "y1[1] (numeric) ", 33, numeric_val, abserr 100.0 20, " "), if abs(analytic_val_y) # 0.0 then relerr : ------------------- abs(analytic_val_y) else relerr : - 1.0, if glob_iter = 1 then array_1st_rel_error : relerr 1 else array_last_rel_error : relerr, omniout_float(ALWAYS, 1 "absolute error ", 4, abserr, 20, " "), omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"), omniout_float(ALWAYS, "h ", 4, glob_h, 20, " "), analytic_val_y : exact_soln_y2(ind_var), omniout_float(ALWAYS, "y2[1] (analytic) ", 33, analytic_val_y, 20, " "), term_no : 1, numeric_val : array_y2 , term_no abserr : abs(numeric_val - analytic_val_y), omniout_float(ALWAYS, "y2[1] (numeric) ", 33, numeric_val, abserr 100.0 20, " "), if abs(analytic_val_y) # 0.0 then relerr : ------------------- abs(analytic_val_y) else relerr : - 1.0, if glob_iter = 1 then array_1st_rel_error : relerr 2 else array_last_rel_error : relerr, omniout_float(ALWAYS, 2 "absolute error ", 4, abserr, 20, " "), omniout_float(ALWAYS, "relative error ", 4, relerr, 20, "%"), omniout_float(ALWAYS, "h ", 4, glob_h, 20, " ")) (%i4) adjust_for_pole(h_param) := block(hnew : h_param, glob_normmax : glob_small_float, if !array_y1_higher ! > glob_small_float ! 1, 1! then (tmp : !array_y1_higher !, if tmp < glob_normmax ! 1, 1! then glob_normmax : tmp), if !array_y2_higher ! > glob_small_float ! 1, 1! then (tmp : !array_y2_higher !, if tmp < glob_normmax ! 1, 1! then glob_normmax : tmp), if glob_look_poles and (!array_pole ! > glob_small_float) and (array_pole # glob_large_float) ! 1! 1 array_pole 1 then (sz2 : -----------, if sz2 < hnew 10.0 then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."), omniout_str(INFO, "Reached Optimal"), newline(), return(hnew))), if not glob_reached_optimal_h then (glob_reached_optimal_h : true, glob_curr_iter_when_opt : glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(), glob_optimal_start : array_x ), hnew : sz2) 1 (%o4) adjust_for_pole(h_param) := block(hnew : h_param, glob_normmax : glob_small_float, if !array_y1_higher ! > glob_small_float ! 1, 1! then (tmp : !array_y1_higher !, if tmp < glob_normmax ! 1, 1! then glob_normmax : tmp), if !array_y2_higher ! > glob_small_float ! 1, 1! then (tmp : !array_y2_higher !, if tmp < glob_normmax ! 1, 1! then glob_normmax : tmp), if glob_look_poles and (!array_pole ! > glob_small_float) and (array_pole # glob_large_float) ! 1! 1 array_pole 1 then (sz2 : -----------, if sz2 < hnew 10.0 then (omniout_float(INFO, "glob_h adjusted to ", 20, h_param, 12, "due to singularity."), omniout_str(INFO, "Reached Optimal"), newline(), return(hnew))), if not glob_reached_optimal_h then (glob_reached_optimal_h : true, glob_curr_iter_when_opt : glob_current_iter, glob_optimal_clock_start_sec : elapsed_time_seconds(), glob_optimal_start : array_x ), hnew : sz2) 1 (%i5) prog_report(x_start, x_end) := (clock_sec1 : elapsed_time_seconds(), total_clock_sec : convfloat(clock_sec1) - convfloat(glob_orig_start_sec), glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec), left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec) + convfloat(glob_max_sec), expect_sec : comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 convfloat(clock_sec1) - convfloat(glob_orig_start_sec)), opt_clock_sec : convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec), glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 convfloat(opt_clock_sec)), percent_done : comp_percent(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done, 1 omniout_str_noeol(INFO, "Total Elapsed Time "), omniout_timestr(convfloat(total_clock_sec)), omniout_str_noeol(INFO, "Elapsed Time(since restart) "), omniout_timestr(convfloat(glob_clock_sec)), if convfloat(percent_done) < convfloat(100.0) then (omniout_str_noeol(INFO, "Expected Time Remaining "), omniout_timestr(convfloat(expect_sec)), omniout_str_noeol(INFO, "Optimized Time Remaining "), omniout_timestr(convfloat(glob_optimal_expect_sec))), omniout_str_noeol(INFO, "Time to Timeout "), omniout_timestr(convfloat(left_sec)), omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%")) (%o5) prog_report(x_start, x_end) := (clock_sec1 : elapsed_time_seconds(), total_clock_sec : convfloat(clock_sec1) - convfloat(glob_orig_start_sec), glob_clock_sec : convfloat(clock_sec1) - convfloat(glob_clock_start_sec), left_sec : - convfloat(clock_sec1) + convfloat(glob_orig_start_sec) + convfloat(glob_max_sec), expect_sec : comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 convfloat(clock_sec1) - convfloat(glob_orig_start_sec)), opt_clock_sec : convfloat(clock_sec1) - convfloat(glob_optimal_clock_start_sec), glob_optimal_expect_sec : comp_expect_sec(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x ), 1 convfloat(opt_clock_sec)), percent_done : comp_percent(convfloat(x_end), convfloat(x_start), convfloat(glob_h) + convfloat(array_x )), glob_percent_done : percent_done, 1 omniout_str_noeol(INFO, "Total Elapsed Time "), omniout_timestr(convfloat(total_clock_sec)), omniout_str_noeol(INFO, "Elapsed Time(since restart) "), omniout_timestr(convfloat(glob_clock_sec)), if convfloat(percent_done) < convfloat(100.0) then (omniout_str_noeol(INFO, "Expected Time Remaining "), omniout_timestr(convfloat(expect_sec)), omniout_str_noeol(INFO, "Optimized Time Remaining "), omniout_timestr(convfloat(glob_optimal_expect_sec))), omniout_str_noeol(INFO, "Time to Timeout "), omniout_timestr(convfloat(left_sec)), omniout_float(INFO, "Percent Done ", 33, percent_done, 4, "%")) (%i6) check_for_pole() := (n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10) and ((!array_y1_higher ! < glob_small_float) ! 1, m! or (!array_y1_higher ! < glob_small_float) ! 1, m - 1! or (!array_y1_higher ! < glob_small_float)) do m : ! 1, m - 2! array_y1_higher 1, m m - 1, if m > 10 then (rm0 : -----------------------, array_y1_higher 1, m - 1 array_y1_higher 1, m - 1 rm1 : -----------------------, hdrc : convfloat(m - 1) rm0 array_y1_higher 1, m - 2 - convfloat(m - 2) rm1, if abs(hdrc) > glob_small_float glob_h convfloat(m - 1) rm0 then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------, hdrc hdrc array_real_pole : rcs, array_real_pole : ord_no) 1, 1 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : glob_large_float)) 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : glob_large_float), n : glob_max_terms, m : - 1 - 1 + n, 1, 2 while (m >= 10) and ((!array_y2_higher ! < glob_small_float) ! 1, m! or (!array_y2_higher ! < glob_small_float) ! 1, m - 1! or (!array_y2_higher ! < glob_small_float)) do m : ! 1, m - 2! array_y2_higher 1, m m - 1, if m > 10 then (rm0 : -----------------------, array_y2_higher 1, m - 1 array_y2_higher 1, m - 1 rm1 : -----------------------, hdrc : convfloat(m - 1) rm0 array_y2_higher 1, m - 2 - convfloat(m - 2) rm1, if abs(hdrc) > glob_small_float glob_h convfloat(m - 1) rm0 then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------, hdrc hdrc array_real_pole : rcs, array_real_pole : ord_no) 2, 1 2, 2 else (array_real_pole : glob_large_float, 2, 1 array_real_pole : glob_large_float)) 2, 2 else (array_real_pole : glob_large_float, 2, 1 array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms, 2, 2 cnt : 0, while (cnt < 5) and (n >= 10) do (if !array_y1_higher ! > ! 1, n! glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n, if m <= 10 then (array_complex_pole : glob_large_float, 1, 1 array_complex_pole : glob_large_float) 1, 2 elseif (!array_y1_higher ! >= glob_large_float) ! 1, m! or (!array_y1_higher ! >= glob_large_float) ! 1, m - 1! or (!array_y1_higher ! >= glob_large_float) ! 1, m - 2! or (!array_y1_higher ! >= glob_large_float) ! 1, m - 3! or (!array_y1_higher ! >= glob_large_float) ! 1, m - 4! or (!array_y1_higher ! >= glob_large_float) ! 1, m - 5! then (array_complex_pole : glob_large_float, 1, 1 array_complex_pole : glob_large_float) 1, 2 array_y1_higher array_y1_higher 1, m 1, m - 1 else (rm0 : -----------------------, rm1 : -----------------------, array_y1_higher array_y1_higher 1, m - 1 1, m - 2 array_y1_higher array_y1_higher 1, m - 2 1, m - 3 rm2 : -----------------------, rm3 : -----------------------, array_y1_higher array_y1_higher 1, m - 3 1, m - 4 array_y1_higher 1, m - 4 rm4 : -----------------------, nr1 : convfloat(m - 3) rm2 array_y1_higher 1, m - 5 - 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0, nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1, - 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0 dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---, rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1 5.0 8.0 3.0 ds2 : --- - --- + ---, if (abs(nr1 dr2 - nr2 dr1) <= glob_small_float) rm4 rm3 rm2 or (abs(dr1) <= glob_small_float) then (array_complex_pole : 1, 1 glob_large_float, array_complex_pole : glob_large_float) 1, 2 else (if abs(nr1 dr2 - nr2 dr1) > glob_small_float dr1 dr2 - ds2 dr1 + ds1 dr2 then (rcs : ---------------------------, nr1 dr2 - nr2 dr1 rcs nr1 - ds1 convfloat(m) ord_no : ------------- - ------------, 2.0 dr1 2.0 if abs(rcs) > glob_small_float then (if rcs > 0.0 then rad_c : sqrt(rcs) glob_h else rad_c : glob_large_float) else (rad_c : glob_large_float, ord_no : glob_large_float)) else (rad_c : glob_large_float, ord_no : glob_large_float)), array_complex_pole : rad_c, 1, 1 array_complex_pole : ord_no), n : - 1 - 1 + glob_max_terms, cnt : 0, 1, 2 while (cnt < 5) and (n >= 10) do (if !array_y2_higher ! > glob_small_float ! 1, n! then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n, if m <= 10 then (array_complex_pole : glob_large_float, 2, 1 array_complex_pole : glob_large_float) 2, 2 elseif (!array_y2_higher ! >= glob_large_float) ! 1, m! or (!array_y2_higher ! >= glob_large_float) ! 1, m - 1! or (!array_y2_higher ! >= glob_large_float) ! 1, m - 2! or (!array_y2_higher ! >= glob_large_float) ! 1, m - 3! or (!array_y2_higher ! >= glob_large_float) ! 1, m - 4! or (!array_y2_higher ! >= glob_large_float) ! 1, m - 5! then (array_complex_pole : glob_large_float, 2, 1 array_complex_pole : glob_large_float) 2, 2 array_y2_higher array_y2_higher 1, m 1, m - 1 else (rm0 : -----------------------, rm1 : -----------------------, array_y2_higher array_y2_higher 1, m - 1 1, m - 2 array_y2_higher array_y2_higher 1, m - 2 1, m - 3 rm2 : -----------------------, rm3 : -----------------------, array_y2_higher array_y2_higher 1, m - 3 1, m - 4 array_y2_higher 1, m - 4 rm4 : -----------------------, nr1 : convfloat(m - 3) rm2 array_y2_higher 1, m - 5 - 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0, nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1, - 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0 dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---, rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1 5.0 8.0 3.0 ds2 : --- - --- + ---, if (abs(nr1 dr2 - nr2 dr1) <= glob_small_float) rm4 rm3 rm2 or (abs(dr1) <= glob_small_float) then (array_complex_pole : 2, 1 glob_large_float, array_complex_pole : glob_large_float) 2, 2 else (if abs(nr1 dr2 - nr2 dr1) > glob_small_float dr1 dr2 - ds2 dr1 + ds1 dr2 then (rcs : ---------------------------, nr1 dr2 - nr2 dr1 rcs nr1 - ds1 convfloat(m) ord_no : ------------- - ------------, 2.0 dr1 2.0 if abs(rcs) > glob_small_float then (if rcs > 0.0 then rad_c : sqrt(rcs) glob_h else rad_c : glob_large_float) else (rad_c : glob_large_float, ord_no : glob_large_float)) else (rad_c : glob_large_float, ord_no : glob_large_float)), array_complex_pole : rad_c, 2, 1 array_complex_pole : ord_no), found : false, 2, 2 if (not found) and ((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float)) 1, 1 1, 2 and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0)) 1, 1 1, 2 then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , found : true, array_type_pole : 2, 1, 2 1, 2 1 if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used")), if (not found) and ((array_real_pole # glob_large_float) and (array_real_pole # glob_large_float) 1, 1 1, 2 and (array_real_pole > 0.0) and (array_real_pole > 0.0) 1, 1 1, 2 and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 0.0))) 1, 1 1, 2 1, 1 1, 2 then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found : true, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")), if (not found) and (((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float))) 1, 1 1, 2 then (array_poles : glob_large_float, array_poles : glob_large_float, 1, 1 1, 2 found : true, array_type_pole : 3, if glob_display_flag 1 then omniout_str(ALWAYS, "NO POLE")), if (not found) and ((array_real_pole < array_complex_pole ) 1, 1 1, 1 and (array_real_pole > 0.0) and (array_real_pole > 1, 1 1, 2 0.0)) then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found : true, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")), if (not found) and ((array_complex_pole # glob_large_float) 1, 1 and (array_complex_pole # glob_large_float) 1, 2 and (array_complex_pole > 0.0) and (array_complex_pole > 1, 1 1, 2 0.0)) then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , array_type_pole : 2, found : true, 1, 2 1, 2 1 if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used")), if not found then (array_poles : glob_large_float, array_poles : glob_large_float, 1, 1 1, 2 array_type_pole : 3, if glob_display_flag 1 then omniout_str(ALWAYS, "NO POLE")), found : false, if (not found) and ((array_real_pole = glob_large_float) 2, 1 or (array_real_pole = glob_large_float)) 2, 2 and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float)) 2, 1 2, 2 and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0)) 2, 1 2, 2 then (array_poles : array_complex_pole , 2, 1 2, 1 array_poles : array_complex_pole , found : true, array_type_pole : 2, 2, 2 2, 2 2 if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used")), if (not found) and ((array_real_pole # glob_large_float) and (array_real_pole # glob_large_float) 2, 1 2, 2 and (array_real_pole > 0.0) and (array_real_pole > 0.0) 2, 1 2, 2 and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 0.0))) 2, 1 2, 2 2, 1 2, 2 then (array_poles : array_real_pole , 2, 1 2, 1 array_poles : array_real_pole , found : true, array_type_pole : 1, 2, 2 2, 2 2 if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")), if (not found) and (((array_real_pole = glob_large_float) 2, 1 or (array_real_pole = glob_large_float)) 2, 2 and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float))) 2, 1 2, 2 then (array_poles : glob_large_float, array_poles : glob_large_float, 2, 1 2, 2 found : true, array_type_pole : 3, if glob_display_flag 2 then omniout_str(ALWAYS, "NO POLE")), if (not found) and ((array_real_pole < array_complex_pole ) 2, 1 2, 1 and (array_real_pole > 0.0) and (array_real_pole > 2, 1 2, 2 0.0)) then (array_poles : array_real_pole , 2, 1 2, 1 array_poles : array_real_pole , found : true, array_type_pole : 1, 2, 2 2, 2 2 if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")), if (not found) and ((array_complex_pole # glob_large_float) 2, 1 and (array_complex_pole # glob_large_float) 2, 2 and (array_complex_pole > 0.0) and (array_complex_pole > 2, 1 2, 2 0.0)) then (array_poles : array_complex_pole , 2, 1 2, 1 array_poles : array_complex_pole , array_type_pole : 2, found : true, 2, 2 2, 2 2 if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used")), if not found then (array_poles : glob_large_float, array_poles : glob_large_float, 2, 1 2, 2 array_type_pole : 3, if glob_display_flag 2 then omniout_str(ALWAYS, "NO POLE")), array_pole : glob_large_float, 1 array_pole : glob_large_float, if array_pole > array_poles 2 1 1, 1 then (array_pole : array_poles , array_pole : array_poles ), 1 1, 1 2 1, 2 if array_pole > array_poles then (array_pole : array_poles , 1 2, 1 1 2, 1 array_pole : array_poles ), display_pole()) 2 2, 2 (%o6) check_for_pole() := (n : glob_max_terms, m : - 1 - 1 + n, while (m >= 10) and ((!array_y1_higher ! < glob_small_float) ! 1, m! or (!array_y1_higher ! < glob_small_float) ! 1, m - 1! or (!array_y1_higher ! < glob_small_float)) do m : ! 1, m - 2! array_y1_higher 1, m m - 1, if m > 10 then (rm0 : -----------------------, array_y1_higher 1, m - 1 array_y1_higher 1, m - 1 rm1 : -----------------------, hdrc : convfloat(m - 1) rm0 array_y1_higher 1, m - 2 - convfloat(m - 2) rm1, if abs(hdrc) > glob_small_float glob_h convfloat(m - 1) rm0 then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------, hdrc hdrc array_real_pole : rcs, array_real_pole : ord_no) 1, 1 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : glob_large_float)) 1, 2 else (array_real_pole : glob_large_float, 1, 1 array_real_pole : glob_large_float), n : glob_max_terms, m : - 1 - 1 + n, 1, 2 while (m >= 10) and ((!array_y2_higher ! < glob_small_float) ! 1, m! or (!array_y2_higher ! < glob_small_float) ! 1, m - 1! or (!array_y2_higher ! < glob_small_float)) do m : ! 1, m - 2! array_y2_higher 1, m m - 1, if m > 10 then (rm0 : -----------------------, array_y2_higher 1, m - 1 array_y2_higher 1, m - 1 rm1 : -----------------------, hdrc : convfloat(m - 1) rm0 array_y2_higher 1, m - 2 - convfloat(m - 2) rm1, if abs(hdrc) > glob_small_float glob_h convfloat(m - 1) rm0 then (rcs : ------, ord_no : 2.0 - convfloat(m) + --------------------, hdrc hdrc array_real_pole : rcs, array_real_pole : ord_no) 2, 1 2, 2 else (array_real_pole : glob_large_float, 2, 1 array_real_pole : glob_large_float)) 2, 2 else (array_real_pole : glob_large_float, 2, 1 array_real_pole : glob_large_float), n : - 1 - 1 + glob_max_terms, 2, 2 cnt : 0, while (cnt < 5) and (n >= 10) do (if !array_y1_higher ! > ! 1, n! glob_small_float then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n, if m <= 10 then (array_complex_pole : glob_large_float, 1, 1 array_complex_pole : glob_large_float) 1, 2 elseif (!array_y1_higher ! >= glob_large_float) ! 1, m! or (!array_y1_higher ! >= glob_large_float) ! 1, m - 1! or (!array_y1_higher ! >= glob_large_float) ! 1, m - 2! or (!array_y1_higher ! >= glob_large_float) ! 1, m - 3! or (!array_y1_higher ! >= glob_large_float) ! 1, m - 4! or (!array_y1_higher ! >= glob_large_float) ! 1, m - 5! then (array_complex_pole : glob_large_float, 1, 1 array_complex_pole : glob_large_float) 1, 2 array_y1_higher array_y1_higher 1, m 1, m - 1 else (rm0 : -----------------------, rm1 : -----------------------, array_y1_higher array_y1_higher 1, m - 1 1, m - 2 array_y1_higher array_y1_higher 1, m - 2 1, m - 3 rm2 : -----------------------, rm3 : -----------------------, array_y1_higher array_y1_higher 1, m - 3 1, m - 4 array_y1_higher 1, m - 4 rm4 : -----------------------, nr1 : convfloat(m - 3) rm2 array_y1_higher 1, m - 5 - 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0, nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1, - 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0 dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---, rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1 5.0 8.0 3.0 ds2 : --- - --- + ---, if (abs(nr1 dr2 - nr2 dr1) <= glob_small_float) rm4 rm3 rm2 or (abs(dr1) <= glob_small_float) then (array_complex_pole : 1, 1 glob_large_float, array_complex_pole : glob_large_float) 1, 2 else (if abs(nr1 dr2 - nr2 dr1) > glob_small_float dr1 dr2 - ds2 dr1 + ds1 dr2 then (rcs : ---------------------------, nr1 dr2 - nr2 dr1 rcs nr1 - ds1 convfloat(m) ord_no : ------------- - ------------, 2.0 dr1 2.0 if abs(rcs) > glob_small_float then (if rcs > 0.0 then rad_c : sqrt(rcs) glob_h else rad_c : glob_large_float) else (rad_c : glob_large_float, ord_no : glob_large_float)) else (rad_c : glob_large_float, ord_no : glob_large_float)), array_complex_pole : rad_c, 1, 1 array_complex_pole : ord_no), n : - 1 - 1 + glob_max_terms, cnt : 0, 1, 2 while (cnt < 5) and (n >= 10) do (if !array_y2_higher ! > glob_small_float ! 1, n! then cnt : 1 + cnt else cnt : 0, n : n - 1), m : cnt + n, if m <= 10 then (array_complex_pole : glob_large_float, 2, 1 array_complex_pole : glob_large_float) 2, 2 elseif (!array_y2_higher ! >= glob_large_float) ! 1, m! or (!array_y2_higher ! >= glob_large_float) ! 1, m - 1! or (!array_y2_higher ! >= glob_large_float) ! 1, m - 2! or (!array_y2_higher ! >= glob_large_float) ! 1, m - 3! or (!array_y2_higher ! >= glob_large_float) ! 1, m - 4! or (!array_y2_higher ! >= glob_large_float) ! 1, m - 5! then (array_complex_pole : glob_large_float, 2, 1 array_complex_pole : glob_large_float) 2, 2 array_y2_higher array_y2_higher 1, m 1, m - 1 else (rm0 : -----------------------, rm1 : -----------------------, array_y2_higher array_y2_higher 1, m - 1 1, m - 2 array_y2_higher array_y2_higher 1, m - 2 1, m - 3 rm2 : -----------------------, rm3 : -----------------------, array_y2_higher array_y2_higher 1, m - 3 1, m - 4 array_y2_higher 1, m - 4 rm4 : -----------------------, nr1 : convfloat(m - 3) rm2 array_y2_higher 1, m - 5 - 2.0 convfloat(m - 2) rm1 + convfloat(m - 1) rm0, nr2 : convfloat(m - 4) rm3 - 2.0 convfloat(m - 3) rm2 + convfloat(m - 2) rm1, - 1.0 2.0 - 1.0 - 1.0 2.0 - 1.0 5.0 8.0 3.0 dr1 : ----- + --- + -----, dr2 : ----- + --- + -----, ds1 : --- - --- + ---, rm3 rm2 rm1 rm4 rm3 rm2 rm3 rm2 rm1 5.0 8.0 3.0 ds2 : --- - --- + ---, if (abs(nr1 dr2 - nr2 dr1) <= glob_small_float) rm4 rm3 rm2 or (abs(dr1) <= glob_small_float) then (array_complex_pole : 2, 1 glob_large_float, array_complex_pole : glob_large_float) 2, 2 else (if abs(nr1 dr2 - nr2 dr1) > glob_small_float dr1 dr2 - ds2 dr1 + ds1 dr2 then (rcs : ---------------------------, nr1 dr2 - nr2 dr1 rcs nr1 - ds1 convfloat(m) ord_no : ------------- - ------------, 2.0 dr1 2.0 if abs(rcs) > glob_small_float then (if rcs > 0.0 then rad_c : sqrt(rcs) glob_h else rad_c : glob_large_float) else (rad_c : glob_large_float, ord_no : glob_large_float)) else (rad_c : glob_large_float, ord_no : glob_large_float)), array_complex_pole : rad_c, 2, 1 array_complex_pole : ord_no), found : false, 2, 2 if (not found) and ((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float)) 1, 1 1, 2 and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0)) 1, 1 1, 2 then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , found : true, array_type_pole : 2, 1, 2 1, 2 1 if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used")), if (not found) and ((array_real_pole # glob_large_float) and (array_real_pole # glob_large_float) 1, 1 1, 2 and (array_real_pole > 0.0) and (array_real_pole > 0.0) 1, 1 1, 2 and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 0.0))) 1, 1 1, 2 1, 1 1, 2 then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found : true, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")), if (not found) and (((array_real_pole = glob_large_float) 1, 1 or (array_real_pole = glob_large_float)) 1, 2 and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float))) 1, 1 1, 2 then (array_poles : glob_large_float, array_poles : glob_large_float, 1, 1 1, 2 found : true, array_type_pole : 3, if glob_display_flag 1 then omniout_str(ALWAYS, "NO POLE")), if (not found) and ((array_real_pole < array_complex_pole ) 1, 1 1, 1 and (array_real_pole > 0.0) and (array_real_pole > 1, 1 1, 2 0.0)) then (array_poles : array_real_pole , 1, 1 1, 1 array_poles : array_real_pole , found : true, array_type_pole : 1, 1, 2 1, 2 1 if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")), if (not found) and ((array_complex_pole # glob_large_float) 1, 1 and (array_complex_pole # glob_large_float) 1, 2 and (array_complex_pole > 0.0) and (array_complex_pole > 1, 1 1, 2 0.0)) then (array_poles : array_complex_pole , 1, 1 1, 1 array_poles : array_complex_pole , array_type_pole : 2, found : true, 1, 2 1, 2 1 if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used")), if not found then (array_poles : glob_large_float, array_poles : glob_large_float, 1, 1 1, 2 array_type_pole : 3, if glob_display_flag 1 then omniout_str(ALWAYS, "NO POLE")), found : false, if (not found) and ((array_real_pole = glob_large_float) 2, 1 or (array_real_pole = glob_large_float)) 2, 2 and ((array_complex_pole # glob_large_float) and (array_complex_pole # glob_large_float)) 2, 1 2, 2 and ((array_complex_pole > 0.0) and (array_complex_pole > 0.0)) 2, 1 2, 2 then (array_poles : array_complex_pole , 2, 1 2, 1 array_poles : array_complex_pole , found : true, array_type_pole : 2, 2, 2 2, 2 2 if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used")), if (not found) and ((array_real_pole # glob_large_float) and (array_real_pole # glob_large_float) 2, 1 2, 2 and (array_real_pole > 0.0) and (array_real_pole > 0.0) 2, 1 2, 2 and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float) or (array_complex_pole <= 0.0) or (array_complex_pole <= 0.0))) 2, 1 2, 2 2, 1 2, 2 then (array_poles : array_real_pole , 2, 1 2, 1 array_poles : array_real_pole , found : true, array_type_pole : 1, 2, 2 2, 2 2 if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")), if (not found) and (((array_real_pole = glob_large_float) 2, 1 or (array_real_pole = glob_large_float)) 2, 2 and ((array_complex_pole = glob_large_float) or (array_complex_pole = glob_large_float))) 2, 1 2, 2 then (array_poles : glob_large_float, array_poles : glob_large_float, 2, 1 2, 2 found : true, array_type_pole : 3, if glob_display_flag 2 then omniout_str(ALWAYS, "NO POLE")), if (not found) and ((array_real_pole < array_complex_pole ) 2, 1 2, 1 and (array_real_pole > 0.0) and (array_real_pole > 2, 1 2, 2 0.0)) then (array_poles : array_real_pole , 2, 1 2, 1 array_poles : array_real_pole , found : true, array_type_pole : 1, 2, 2 2, 2 2 if glob_display_flag then omniout_str(ALWAYS, "Real estimate of pole used")), if (not found) and ((array_complex_pole # glob_large_float) 2, 1 and (array_complex_pole # glob_large_float) 2, 2 and (array_complex_pole > 0.0) and (array_complex_pole > 2, 1 2, 2 0.0)) then (array_poles : array_complex_pole , 2, 1 2, 1 array_poles : array_complex_pole , array_type_pole : 2, found : true, 2, 2 2, 2 2 if glob_display_flag then omniout_str(ALWAYS, "Complex estimate of poles used")), if not found then (array_poles : glob_large_float, array_poles : glob_large_float, 2, 1 2, 2 array_type_pole : 3, if glob_display_flag 2 then omniout_str(ALWAYS, "NO POLE")), array_pole : glob_large_float, 1 array_pole : glob_large_float, if array_pole > array_poles 2 1 1, 1 then (array_pole : array_poles , array_pole : array_poles ), 1 1, 1 2 1, 2 if array_pole > array_poles then (array_pole : array_poles , 1 2, 1 1 2, 1 array_pole : array_poles ), display_pole()) 2 2, 2 (%i7) get_norms() := if not glob_initial_pass then (set_z(array_norms, 1 + glob_max_terms), iii : 1, while iii <= glob_max_terms do (if !array_y1 ! > array_norms ! iii! iii then array_norms : !array_y1 !, iii : 1 + iii), iii : 1, iii ! iii! while iii <= glob_max_terms do (if !array_y2 ! > array_norms ! iii! iii then array_norms : !array_y2 !, iii : 1 + iii)) iii ! iii! (%o7) get_norms() := if not glob_initial_pass then (set_z(array_norms, 1 + glob_max_terms), iii : 1, while iii <= glob_max_terms do (if !array_y1 ! > array_norms ! iii! iii then array_norms : !array_y1 !, iii : 1 + iii), iii : 1, iii ! iii! while iii <= glob_max_terms do (if !array_y2 ! > array_norms ! iii! iii then array_norms : !array_y2 !, iii : 1 + iii)) iii ! iii! (%i8) atomall() := (array_tmp1 : array_y2_higher , 1 6, 1 array_tmp2 : array_tmp1 + array_const_0D0 , 1 1 1 if not array_y1_set_initial then (if 1 <= glob_max_terms 1, 2 1 then (temporary : array_tmp2 glob_h factorial_3(0, 1), 1 array_y1 : temporary, array_y1_higher : temporary, 2 1, 2 temporary 2.0 temporary : -------------, array_y1_higher : temporary)), kkk : 2, glob_h 2, 1 array_tmp4 : array_y1 - array_const_2D0 , 1 1 1 if not array_y2_set_initial then (if 1 <= glob_max_terms 2, 2 1 then (temporary : array_tmp4 glob_h factorial_3(0, 1), 1 array_y2 : temporary, array_y2_higher : temporary, 2 1, 2 temporary 2.0 temporary : -------------, array_y2_higher : temporary)), kkk : 2, glob_h 2, 1 array_tmp1 : array_y2_higher , array_tmp2 : 2 6, 2 2 array_tmp1 + array_const_0D0 , if not array_y1_set_initial 2 2 1, 3 then (if 2 <= glob_max_terms then (temporary : 1 array_tmp2 glob_h factorial_3(1, 2), array_y1 : temporary, 2 3 temporary 2.0 array_y1_higher : temporary, temporary : -------------, 1, 3 glob_h array_y1_higher : temporary)), kkk : 3, 2, 2 array_tmp4 : array_y1 - array_const_2D0 , 2 2 2 if not array_y2_set_initial then (if 2 <= glob_max_terms 2, 3 1 then (temporary : array_tmp4 glob_h factorial_3(1, 2), 2 array_y2 : temporary, array_y2_higher : temporary, 3 1, 3 temporary 2.0 temporary : -------------, array_y2_higher : temporary)), kkk : 3, glob_h 2, 2 array_tmp1 : array_y2_higher , array_tmp2 : 3 6, 3 3 array_tmp1 + array_const_0D0 , if not array_y1_set_initial 3 3 1, 4 then (if 3 <= glob_max_terms then (temporary : 1 array_tmp2 glob_h factorial_3(2, 3), array_y1 : temporary, 3 4 temporary 2.0 array_y1_higher : temporary, temporary : -------------, 1, 4 glob_h array_y1_higher : temporary)), kkk : 4, 2, 3 array_tmp4 : array_y1 - array_const_2D0 , 3 3 3 if not array_y2_set_initial then (if 3 <= glob_max_terms 2, 4 1 then (temporary : array_tmp4 glob_h factorial_3(2, 3), 3 array_y2 : temporary, array_y2_higher : temporary, 4 1, 4 temporary 2.0 temporary : -------------, array_y2_higher : temporary)), kkk : 4, glob_h 2, 3 array_tmp1 : array_y2_higher , array_tmp2 : 4 6, 4 4 array_tmp1 + array_const_0D0 , if not array_y1_set_initial 4 4 1, 5 then (if 4 <= glob_max_terms then (temporary : 1 array_tmp2 glob_h factorial_3(3, 4), array_y1 : temporary, 4 5 temporary 2.0 array_y1_higher : temporary, temporary : -------------, 1, 5 glob_h array_y1_higher : temporary)), kkk : 5, 2, 4 array_tmp4 : array_y1 - array_const_2D0 , 4 4 4 if not array_y2_set_initial then (if 4 <= glob_max_terms 2, 5 1 then (temporary : array_tmp4 glob_h factorial_3(3, 4), 4 array_y2 : temporary, array_y2_higher : temporary, 5 1, 5 temporary 2.0 temporary : -------------, array_y2_higher : temporary)), kkk : 5, glob_h 2, 4 array_tmp1 : array_y2_higher , array_tmp2 : 5 6, 5 5 array_tmp1 + array_const_0D0 , if not array_y1_set_initial 5 5 1, 6 then (if 5 <= glob_max_terms then (temporary : 1 array_tmp2 glob_h factorial_3(4, 5), array_y1 : temporary, 5 6 temporary 2.0 array_y1_higher : temporary, temporary : -------------, 1, 6 glob_h array_y1_higher : temporary)), kkk : 6, 2, 5 array_tmp4 : array_y1 - array_const_2D0 , 5 5 5 if not array_y2_set_initial then (if 5 <= glob_max_terms 2, 6 1 then (temporary : array_tmp4 glob_h factorial_3(4, 5), 5 array_y2 : temporary, array_y2_higher : temporary, 6 1, 6 temporary 2.0 temporary : -------------, array_y2_higher : temporary)), kkk : 6, glob_h 2, 5 while kkk <= glob_max_terms do (array_tmp1 : array_y2_higher , kkk 6, kkk array_tmp2 : array_tmp1 + array_const_0D0 , order_d : 1, kkk kkk kkk if 1 + order_d + kkk <= glob_max_terms then (if not array_y1_set_initial 1, order_d + kkk order_d array_tmp2 glob_h kkk then (temporary : -----------------------------------------, factorial_3(kkk - 1, - 1 + order_d + kkk) array_y1 : temporary, array_y1_higher : order_d + kkk 1, order_d + kkk temporary, term : - 1 + order_d + kkk, adj2 : 2, while (adj2 <= 1 + order_d) and (term >= 1) do (temporary : temporary convfp(adj2) ----------------------, array_y1_higher : temporary, glob_h adj2, term adj2 : 1 + adj2, term : term - 1))), array_tmp4 : kkk array_y1 - array_const_2D0 , order_d : 1, kkk kkk if 1 + order_d + kkk <= glob_max_terms then (if not array_y2_set_initial 2, order_d + kkk order_d array_tmp4 glob_h kkk then (temporary : -----------------------------------------, factorial_3(kkk - 1, - 1 + order_d + kkk) array_y2 : temporary, array_y2_higher : order_d + kkk 1, order_d + kkk temporary, term : - 1 + order_d + kkk, adj2 : 2, while (adj2 <= 1 + order_d) and (term >= 1) do (temporary : temporary convfp(adj2) ----------------------, array_y2_higher : temporary, glob_h adj2, term adj2 : 1 + adj2, term : term - 1))), kkk : 1 + kkk)) (%o8) atomall() := (array_tmp1 : array_y2_higher , 1 6, 1 array_tmp2 : array_tmp1 + array_const_0D0 , 1 1 1 if not array_y1_set_initial then (if 1 <= glob_max_terms 1, 2 1 then (temporary : array_tmp2 glob_h factorial_3(0, 1), 1 array_y1 : temporary, array_y1_higher : temporary, 2 1, 2 temporary 2.0 temporary : -------------, array_y1_higher : temporary)), kkk : 2, glob_h 2, 1 array_tmp4 : array_y1 - array_const_2D0 , 1 1 1 if not array_y2_set_initial then (if 1 <= glob_max_terms 2, 2 1 then (temporary : array_tmp4 glob_h factorial_3(0, 1), 1 array_y2 : temporary, array_y2_higher : temporary, 2 1, 2 temporary 2.0 temporary : -------------, array_y2_higher : temporary)), kkk : 2, glob_h 2, 1 array_tmp1 : array_y2_higher , array_tmp2 : 2 6, 2 2 array_tmp1 + array_const_0D0 , if not array_y1_set_initial 2 2 1, 3 then (if 2 <= glob_max_terms then (temporary : 1 array_tmp2 glob_h factorial_3(1, 2), array_y1 : temporary, 2 3 temporary 2.0 array_y1_higher : temporary, temporary : -------------, 1, 3 glob_h array_y1_higher : temporary)), kkk : 3, 2, 2 array_tmp4 : array_y1 - array_const_2D0 , 2 2 2 if not array_y2_set_initial then (if 2 <= glob_max_terms 2, 3 1 then (temporary : array_tmp4 glob_h factorial_3(1, 2), 2 array_y2 : temporary, array_y2_higher : temporary, 3 1, 3 temporary 2.0 temporary : -------------, array_y2_higher : temporary)), kkk : 3, glob_h 2, 2 array_tmp1 : array_y2_higher , array_tmp2 : 3 6, 3 3 array_tmp1 + array_const_0D0 , if not array_y1_set_initial 3 3 1, 4 then (if 3 <= glob_max_terms then (temporary : 1 array_tmp2 glob_h factorial_3(2, 3), array_y1 : temporary, 3 4 temporary 2.0 array_y1_higher : temporary, temporary : -------------, 1, 4 glob_h array_y1_higher : temporary)), kkk : 4, 2, 3 array_tmp4 : array_y1 - array_const_2D0 , 3 3 3 if not array_y2_set_initial then (if 3 <= glob_max_terms 2, 4 1 then (temporary : array_tmp4 glob_h factorial_3(2, 3), 3 array_y2 : temporary, array_y2_higher : temporary, 4 1, 4 temporary 2.0 temporary : -------------, array_y2_higher : temporary)), kkk : 4, glob_h 2, 3 array_tmp1 : array_y2_higher , array_tmp2 : 4 6, 4 4 array_tmp1 + array_const_0D0 , if not array_y1_set_initial 4 4 1, 5 then (if 4 <= glob_max_terms then (temporary : 1 array_tmp2 glob_h factorial_3(3, 4), array_y1 : temporary, 4 5 temporary 2.0 array_y1_higher : temporary, temporary : -------------, 1, 5 glob_h array_y1_higher : temporary)), kkk : 5, 2, 4 array_tmp4 : array_y1 - array_const_2D0 , 4 4 4 if not array_y2_set_initial then (if 4 <= glob_max_terms 2, 5 1 then (temporary : array_tmp4 glob_h factorial_3(3, 4), 4 array_y2 : temporary, array_y2_higher : temporary, 5 1, 5 temporary 2.0 temporary : -------------, array_y2_higher : temporary)), kkk : 5, glob_h 2, 4 array_tmp1 : array_y2_higher , array_tmp2 : 5 6, 5 5 array_tmp1 + array_const_0D0 , if not array_y1_set_initial 5 5 1, 6 then (if 5 <= glob_max_terms then (temporary : 1 array_tmp2 glob_h factorial_3(4, 5), array_y1 : temporary, 5 6 temporary 2.0 array_y1_higher : temporary, temporary : -------------, 1, 6 glob_h array_y1_higher : temporary)), kkk : 6, 2, 5 array_tmp4 : array_y1 - array_const_2D0 , 5 5 5 if not array_y2_set_initial then (if 5 <= glob_max_terms 2, 6 1 then (temporary : array_tmp4 glob_h factorial_3(4, 5), 5 array_y2 : temporary, array_y2_higher : temporary, 6 1, 6 temporary 2.0 temporary : -------------, array_y2_higher : temporary)), kkk : 6, glob_h 2, 5 while kkk <= glob_max_terms do (array_tmp1 : array_y2_higher , kkk 6, kkk array_tmp2 : array_tmp1 + array_const_0D0 , order_d : 1, kkk kkk kkk if 1 + order_d + kkk <= glob_max_terms then (if not array_y1_set_initial 1, order_d + kkk order_d array_tmp2 glob_h kkk then (temporary : -----------------------------------------, factorial_3(kkk - 1, - 1 + order_d + kkk) array_y1 : temporary, array_y1_higher : order_d + kkk 1, order_d + kkk temporary, term : - 1 + order_d + kkk, adj2 : 2, while (adj2 <= 1 + order_d) and (term >= 1) do (temporary : temporary convfp(adj2) ----------------------, array_y1_higher : temporary, glob_h adj2, term adj2 : 1 + adj2, term : term - 1))), array_tmp4 : kkk array_y1 - array_const_2D0 , order_d : 1, kkk kkk if 1 + order_d + kkk <= glob_max_terms then (if not array_y2_set_initial 2, order_d + kkk order_d array_tmp4 glob_h kkk then (temporary : -----------------------------------------, factorial_3(kkk - 1, - 1 + order_d + kkk) array_y2 : temporary, array_y2_higher : order_d + kkk 1, order_d + kkk temporary, term : - 1 + order_d + kkk, adj2 : 2, while (adj2 <= 1 + order_d) and (term >= 1) do (temporary : temporary convfp(adj2) ----------------------, array_y2_higher : temporary, glob_h adj2, term adj2 : 1 + adj2, term : term - 1))), kkk : 1 + kkk)) log(x) (%i9) log10(x) := --------- log(10.0) log(x) (%o9) log10(x) := --------- log(10.0) (%i10) omniout_str(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a~%", string(str)) (%o10) omniout_str(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a~%", string(str)) (%i11) omniout_str_noeol(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a", string(str)) (%o11) omniout_str_noeol(iolevel, str) := if glob_iolevel >= iolevel then printf(true, "~a", string(str)) (%i12) omniout_labstr(iolevel, label, str) := if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label), string(str)) (%o12) omniout_labstr(iolevel, label, str) := if glob_iolevel >= iolevel then printf(true, "~a = ~a~%", string(label), string(str)) (%i13) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (if vallen = 4 then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel) else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)) (%o13) omniout_float(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (if vallen = 4 then printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel) else printf(true, "~a = ~g ~s ~%", prelabel, value, postlabel)) (%i14) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value, postlabel), newline()) (%o14) omniout_int(iolevel, prelabel, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (printf(true, "~a = ~d ~a~%", prelabel, value, postlabel), newline()) (%i15) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline()) (%o15) omniout_float_arr(iolevel, prelabel, elemnt, prelen, value, vallen, postlabel) := if glob_iolevel >= iolevel then (sprint(prelabel, "[", elemnt, "]=", value, postlabel), newline()) (%i16) dump_series(iolevel, dump_label, series_name, array_series, numb) := if glob_iolevel >= iolevel then (i : 1, while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ", array_series ), newline(), i : 1 + i)) i (%o16) dump_series(iolevel, dump_label, series_name, array_series, numb) := if glob_iolevel >= iolevel then (i : 1, while i <= numb do (sprint(dump_label, series_name, "i = ", i, "series = ", array_series ), newline(), i : 1 + i)) i (%i17) dump_series_2(iolevel, dump_label, series_name, array_series2, numb, subnum) := if glob_iolevel >= iolevel then (sub : 1, while sub <= subnum do (i : 1, while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i, "series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub)) sub, i (%o17) dump_series_2(iolevel, dump_label, series_name, array_series2, numb, subnum) := if glob_iolevel >= iolevel then (sub : 1, while sub <= subnum do (i : 1, while i <= num do (sprint(dump_label, series_name, "sub = ", sub, "i = ", i, "series2 = ", array_series2 ), i : 1 + i), sub : 1 + sub)) sub, i (%i18) cs_info(iolevel, str) := if glob_iolevel >= iolevel then sprint(concat("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h)) (%o18) cs_info(iolevel, str) := if glob_iolevel >= iolevel then sprint(concat("cs_info ", str, " glob_correct_start_flag = ", glob_correct_start_flag, "glob_h := ", glob_h, "glob_reached_optimal_h := ", glob_reached_optimal_h)) (%i19) logitem_time(fd, secs_in) := (secs : secs_in, printf(fd, ""), if secs >= 0.0 then (sec_in_millinium : sec_in_min min_in_hour hours_in_day days_in_year years_in_century secs centuries_in_millinium, milliniums : ----------------, sec_in_millinium millinium_int : floor(milliniums), centuries : (milliniums - millinium_int) centuries_in_millinium, cent_int : floor(centuries), years : (centuries - cent_int) years_in_century, years_int : floor(years), days : (years - years_int) days_in_year, days_int : floor(days), hours : (days - days_int) hours_in_day, hours_int : floor(hours), minutes : (hours - hours_int) min_in_hour, minutes_int : floor(minutes), seconds : (minutes - minutes_int) sec_in_min, sec_int : floor(seconds), if millinium_int > 0 then printf(fd, "~d Millinia ~d\ Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elseif cent_int > 0 then printf(fd, "~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elseif years_int > 0 then printf(fd, "~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(fd, "~d Days ~d Hours ~d Minutes ~d Seconds", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(fd, "~d Hours ~d Minutes ~d Seconds", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(fd, "~d Minutes ~d Seconds", minutes_int, sec_int) else printf(fd, "~d Seconds", sec_int)) else printf(fd, "Unknown"), printf(fd, "")) (%o19) logitem_time(fd, secs_in) := (secs : secs_in, printf(fd, ""), if secs >= 0.0 then (sec_in_millinium : sec_in_min min_in_hour hours_in_day days_in_year years_in_century secs centuries_in_millinium, milliniums : ----------------, sec_in_millinium millinium_int : floor(milliniums), centuries : (milliniums - millinium_int) centuries_in_millinium, cent_int : floor(centuries), years : (centuries - cent_int) years_in_century, years_int : floor(years), days : (years - years_int) days_in_year, days_int : floor(days), hours : (days - days_int) hours_in_day, hours_int : floor(hours), minutes : (hours - hours_int) min_in_hour, minutes_int : floor(minutes), seconds : (minutes - minutes_int) sec_in_min, sec_int : floor(seconds), if millinium_int > 0 then printf(fd, "~d Millinia ~d\ Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elseif cent_int > 0 then printf(fd, "~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elseif years_int > 0 then printf(fd, "~d Years ~d Days ~d Hours ~d Minutes ~d Seconds", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(fd, "~d Days ~d Hours ~d Minutes ~d Seconds", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(fd, "~d Hours ~d Minutes ~d Seconds", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(fd, "~d Minutes ~d Seconds", minutes_int, sec_int) else printf(fd, "~d Seconds", sec_int)) else printf(fd, "Unknown"), printf(fd, "")) (%i20) omniout_timestr(secs_in) := (secs : convfloat(secs_in), if secs >= convfloat(0.0) then (sec_in_millinium : convfloat(sec_in_min) convfloat(min_in_hour) convfloat(hours_in_day) convfloat(days_in_year) convfloat(years_in_century) secs convfloat(centuries_in_millinium), milliniums : ---------------------------, convfloat(sec_in_millinium) millinium_int : floor(milliniums), centuries : (milliniums - millinium_int) convfloat(centuries_in_millinium), cent_int : floor(centuries), years : (centuries - cent_int) convfloat(years_in_century), years_int : floor(years), days : (years - years_int) convfloat(days_in_year), days_int : floor(days), hours : (days - days_int) convfloat(hours_in_day), hours_int : floor(hours), minutes : (hours - hours_int) convfloat(min_in_hour), minutes_int : floor(minutes), seconds : (minutes - minutes_int) convfloat(sec_in_min), sec_int : floor(seconds), if millinium_int > 0 then printf(true, "= ~d Millinia ~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elseif cent_int > 0 then printf(true, "= ~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elseif years_int > 0 then printf(true, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%")) (%o20) omniout_timestr(secs_in) := (secs : convfloat(secs_in), if secs >= convfloat(0.0) then (sec_in_millinium : convfloat(sec_in_min) convfloat(min_in_hour) convfloat(hours_in_day) convfloat(days_in_year) convfloat(years_in_century) secs convfloat(centuries_in_millinium), milliniums : ---------------------------, convfloat(sec_in_millinium) millinium_int : floor(milliniums), centuries : (milliniums - millinium_int) convfloat(centuries_in_millinium), cent_int : floor(centuries), years : (centuries - cent_int) convfloat(years_in_century), years_int : floor(years), days : (years - years_int) convfloat(days_in_year), days_int : floor(days), hours : (days - days_int) convfloat(hours_in_day), hours_int : floor(hours), minutes : (hours - hours_int) convfloat(min_in_hour), minutes_int : floor(minutes), seconds : (minutes - minutes_int) convfloat(sec_in_min), sec_int : floor(seconds), if millinium_int > 0 then printf(true, "= ~d Millinia ~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", millinium_int, cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elseif cent_int > 0 then printf(true, "= ~d Centuries ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", cent_int, years_int, days_int, hours_int, minutes_int, sec_int) elseif years_int > 0 then printf(true, "= ~d Years ~d Days ~d Hours ~d Minutes ~d Seconds~%", years_int, days_int, hours_int, minutes_int, sec_int) elseif days_int > 0 then printf(true, "= ~d Days ~d Hours ~d Minutes ~d Seconds~%", days_int, hours_int, minutes_int, sec_int) elseif hours_int > 0 then printf(true, "= ~d Hours ~d Minutes ~d Seconds~%", hours_int, minutes_int, sec_int) elseif minutes_int > 0 then printf(true, "= ~d Minutes ~d Seconds~%", minutes_int, sec_int) else printf(true, "= ~d Seconds~%", sec_int)) else printf(true, " Unknown~%")) (%i21) mode_declare(ats, bfloat) modedeclare: bfloat is not a built-in type; assuming it is a Maxima extension type. (%o21) [ats] (%i22) ats(mmm_ats, array_a, array_b, jjj_ats) := (ret_ats : 0.0, if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats, while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats, ret_ats : array_a array_b + ret_ats, iii_ats : 1 + iii_ats)), iii_ats lll_ats ret_ats) (%o22) ats(mmm_ats, array_a, array_b, jjj_ats) := (ret_ats : 0.0, if jjj_ats <= mmm_ats then (ma_ats : 1 + mmm_ats, iii_ats : jjj_ats, while iii_ats <= mmm_ats do (lll_ats : ma_ats - iii_ats, ret_ats : array_a array_b + ret_ats, iii_ats : 1 + iii_ats)), iii_ats lll_ats ret_ats) (%i23) mode_declare(att, bfloat) modedeclare: bfloat is not a built-in type; assuming it is a Maxima extension type. (%o23) [att] (%i24) att(mmm_att, array_aa, array_bb, jjj_att) := (ret_att : 0.0, if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att, while iii_att <= mmm_att do (lll_att : ma_att - iii_att, al_att : lll_att - 1, if lll_att <= glob_max_terms then ret_att : array_aa array_bb convfp(al_att) + ret_att, iii_att lll_att ret_att iii_att : 1 + iii_att), ret_att : ---------------), ret_att) convfp(mmm_att) (%o24) att(mmm_att, array_aa, array_bb, jjj_att) := (ret_att : 0.0, if jjj_att <= mmm_att then (ma_att : 2 + mmm_att, iii_att : jjj_att, while iii_att <= mmm_att do (lll_att : ma_att - iii_att, al_att : lll_att - 1, if lll_att <= glob_max_terms then ret_att : array_aa array_bb convfp(al_att) + ret_att, iii_att lll_att ret_att iii_att : 1 + iii_att), ret_att : ---------------), ret_att) convfp(mmm_att) (%i25) display_pole() := if (array_pole # glob_large_float) 1 and (array_pole > 0.0) and (array_pole # glob_large_float) 1 2 and (array_pole > 0.0) and glob_display_flag 2 then (omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole , 4, " "), omniout_float(ALWAYS, 1 "Order of pole ", 4, array_pole , 4, " ")) 2 (%o25) display_pole() := if (array_pole # glob_large_float) 1 and (array_pole > 0.0) and (array_pole # glob_large_float) 1 2 and (array_pole > 0.0) and glob_display_flag 2 then (omniout_float(ALWAYS, "Radius of convergence ", 4, array_pole , 4, " "), omniout_float(ALWAYS, 1 "Order of pole ", 4, array_pole , 4, " ")) 2 (%i26) logditto(file) := (printf(file, ""), printf(file, "ditto"), printf(file, "")) (%o26) logditto(file) := (printf(file, ""), printf(file, "ditto"), printf(file, "")) (%i27) logitem_integer(file, n) := (printf(file, ""), printf(file, "~d", n), printf(file, "")) (%o27) logitem_integer(file, n) := (printf(file, ""), printf(file, "~d", n), printf(file, "")) (%i28) logitem_str(file, str) := (printf(file, ""), printf(file, str), printf(file, "")) (%o28) logitem_str(file, str) := (printf(file, ""), printf(file, str), printf(file, "")) (%i29) log_revs(file, revs) := printf(file, revs) (%o29) log_revs(file, revs) := printf(file, revs) (%i30) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x), printf(file, "")) (%o30) logitem_float(file, x) := (printf(file, ""), printf(file, "~g", x), printf(file, "")) (%i31) logitem_pole(file, pole) := (printf(file, ""), if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real") elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"), printf(file, "")) (%o31) logitem_pole(file, pole) := (printf(file, ""), if pole = 0 then printf(file, "NA") elseif pole = 1 then printf(file, "Real") elseif pole = 2 then printf(file, "Complex") else printf(file, "No Pole"), printf(file, "")) (%i32) logstart(file) := printf(file, "") (%o32) logstart(file) := printf(file, "") (%i33) logend(file) := printf(file, "~%") (%o33) logend(file) := printf(file, "~%") (%i34) chk_data() := (errflag : false, if (glob_max_terms < 15) or (glob_max_terms > 512) then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"), glob_max_terms : 30), if glob_max_iter < 2 then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true), if errflag then quit()) (%o34) chk_data() := (errflag : false, if (glob_max_terms < 15) or (glob_max_terms > 512) then (omniout_str(ALWAYS, "Illegal max_terms = -- Using 30"), glob_max_terms : 30), if glob_max_iter < 2 then (omniout_str(ALWAYS, "Illegal max_iter"), errflag : true), if errflag then quit()) (%i35) mode_declare(comp_expect_sec, bfloat) modedeclare: bfloat is not a built-in type; assuming it is a Maxima extension type. (%o35) [comp_expect_sec] (%i36) comp_expect_sec(t_end2, t_start2, t2, clock_sec) := (ms2 : clock_sec, sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, if sub1 = 0.0 then sec_left : 0.0 else (if abs(sub2) > 0.0 sub1 then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left) sub2 (%o36) comp_expect_sec(t_end2, t_start2, t2, clock_sec) := (ms2 : clock_sec, sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, if sub1 = 0.0 then sec_left : 0.0 else (if abs(sub2) > 0.0 sub1 then (rrr : ----, sec_left : rrr ms2 - ms2) else sec_left : 0.0), sec_left) sub2 (%i37) mode_declare(comp_percent, bfloat) modedeclare: bfloat is not a built-in type; assuming it is a Maxima extension type. (%o37) [comp_percent] (%i38) comp_percent(t_end2, t_start2, t2) := (sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, 100.0 sub2 if abs(sub2) > glob_small_float then rrr : ---------- else rrr : 0.0, rrr) sub1 (%o38) comp_percent(t_end2, t_start2, t2) := (sub1 : t_end2 - t_start2, sub2 : t2 - t_start2, 100.0 sub2 if abs(sub2) > glob_small_float then rrr : ---------- else rrr : 0.0, rrr) sub1 (%i39) mode_declare(factorial_1, bfloat) modedeclare: bfloat is not a built-in type; assuming it is a Maxima extension type. (%o39) [factorial_1] (%i40) factorial_1(nnn) := nnn! (%o40) factorial_1(nnn) := nnn! (%i41) mode_declare(factorial_3, bfloat) modedeclare: bfloat is not a built-in type; assuming it is a Maxima extension type. (%o41) [factorial_3] mmm2! (%i42) factorial_3(mmm2, nnn2) := ----- nnn2! mmm2! (%o42) factorial_3(mmm2, nnn2) := ----- nnn2! (%i43) convfp(mmm) := mmm (%o43) convfp(mmm) := mmm (%i44) convfloat(mmm) := mmm (%o44) convfloat(mmm) := mmm (%i45) elapsed_time_seconds() := (t : elapsed_real_time(), t) (%o45) elapsed_time_seconds() := (t : elapsed_real_time(), t) (%i46) arcsin(x) := asin(x) (%o46) arcsin(x) := asin(x) (%i47) arccos(x) := acos(x) (%o47) arccos(x) := acos(x) (%i48) arctan(x) := atan(x) (%o48) arctan(x) := atan(x) (%i49) exact_soln_y1(x) := sin(x) + 2.0 (%o49) exact_soln_y1(x) := sin(x) + 2.0 (%i50) exact_soln_y2(x) := 2.0 - cos(x) (%o50) exact_soln_y2(x) := 2.0 - cos(x) (%i51) exact_soln_y2p(x) := sin(x) (%o51) exact_soln_y2p(x) := sin(x) (%i52) exact_soln_y2pp(x) := cos(x) (%o52) exact_soln_y2pp(x) := cos(x) (%i53) exact_soln_y2ppp(x) := - sin(x) (%o53) exact_soln_y2ppp(x) := - sin(x) (%i54) exact_soln_y2pppp(x) := - cos(x) (%o54) exact_soln_y2pppp(x) := - cos(x) (%i55) mainprog() := (define_variable(ALWAYS, 1, fixnum), define_variable(DEBUGL, 3, fixnum), define_variable(glob_iolevel, 5, fixnum), define_variable(glob_max_terms, 30, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(INFO, 2, fixnum), define_variable(glob_no_eqs, 0, fixnum), define_variable(glob_max_hours, 0.0, float), define_variable(glob_look_poles, false, boolean), define_variable(glob_hmax, 1.0, float), define_variable(glob_initial_pass, true, boolean), define_variable(glob_clock_start_sec, 0.0, float), define_variable(centuries_in_millinium, 10.0, float), define_variable(days_in_year, 365.0, float), define_variable(glob_optimal_done, false, boolean), define_variable(glob_dump, false, boolean), define_variable(glob_optimal_expect_sec, 0.1, float), define_variable(glob_abserr, 1.0E-11, float), define_variable(glob_not_yet_start_msg, true, boolean), define_variable(glob_clock_sec, 0.0, float), define_variable(years_in_century, 100.0, float), define_variable(hours_in_day, 24.0, float), define_variable(glob_start, 0, fixnum), define_variable(glob_small_float, 1.0E-51, float), define_variable(glob_log10_relerr, 1.0E-11, float), define_variable(glob_hmin_init, 0.001, float), define_variable(glob_reached_optimal_h, false, boolean), define_variable(glob_html_log, true, boolean), define_variable(glob_max_minutes, 0.0, float), define_variable(glob_max_rel_trunc_err, 1.0E-11, float), define_variable(glob_large_float, 9.0E+100, float), define_variable(glob_almost_1, 0.999, float), define_variable(djd_debug, true, boolean), define_variable(glob_log10abserr, 0.0, float), define_variable(glob_orig_start_sec, 0.0, float), define_variable(glob_last_good_h, 0.1, float), define_variable(glob_disp_incr, 0.1, float), define_variable(min_in_hour, 60.0, float), define_variable(djd_debug2, true, boolean), define_variable(glob_log10relerr, 0.0, float), define_variable(glob_normmax, 0.0, float), define_variable(glob_iter, 0, fixnum), define_variable(glob_max_sec, 10000.0, float), define_variable(glob_warned2, false, boolean), define_variable(glob_max_iter, 1000, fixnum), define_variable(glob_log10_abserr, 1.0E-11, float), define_variable(glob_dump_analytic, false, boolean), define_variable(glob_h, 0.1, float), define_variable(glob_hmin, 1.0E-11, float), define_variable(glob_not_yet_finished, true, boolean), define_variable(sec_in_min, 60.0, float), define_variable(glob_display_flag, true, boolean), define_variable(glob_log10normmin, 0.1, float), define_variable(MAX_UNCHANGED, 10, fixnum), define_variable(glob_current_iter, 0, fixnum), define_variable(glob_unchanged_h_cnt, 0, fixnum), define_variable(glob_smallish_float, 1.0E-101, float), define_variable(glob_optimal_clock_start_sec, 0.0, float), define_variable(glob_relerr, 1.0E-11, float), define_variable(glob_subiter_method, 3, fixnum), define_variable(glob_curr_iter_when_opt, 0, fixnum), define_variable(glob_warned, false, boolean), define_variable(glob_optimal_start, 0.0, float), define_variable(glob_max_trunc_err, 1.0E-11, float), define_variable(glob_max_opt_iter, 10, fixnum), define_variable(glob_percent_done, 0.0, float), ALWAYS : 1, INFO : 2, DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO, glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10, glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 2, glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0, glob_max_minutes : 15.0, omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"), omniout_str(ALWAYS, "##############temp/mtest9postode.ode#################"), omniout_str(ALWAYS, "diff(y1,x,1) = diff(y2,x,5);"), omniout_str(ALWAYS, "diff(y2,x,1) = y1 - 2.0;"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits : 32,"), omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start : 0.5,"), omniout_str(ALWAYS, "x_end : 10.0,"), omniout_str(ALWAYS, "array_y1_init[0 + 1] : exact_soln_y1(x_start),"), omniout_str(ALWAYS, "array_y2_init[0 + 1] : exact_soln_y2(x_start),"), omniout_str(ALWAYS, "array_y2_init[1 + 1] : exact_soln_y2p(x_start),"), omniout_str(ALWAYS, "array_y2_init[2 + 1] : exact_soln_y2pp(x_start),"), omniout_str(ALWAYS, "array_y2_init[3 + 1] : exact_soln_y2ppp(x_start),"), omniout_str(ALWAYS, "array_y2_init[4 + 1] : exact_soln_y2pppp(x_start),"), omniout_str(ALWAYS, "glob_h : 0.00001 ,"), omniout_str(ALWAYS, "glob_look_poles : true,"), omniout_str(ALWAYS, "glob_max_iter : 10,"), omniout_str(ALWAYS, "glob_subiter_method : 3,"), omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"), omniout_str(ALWAYS, "glob_h : 0.0001 ,"), omniout_str(ALWAYS, "glob_look_poles : true,"), omniout_str(ALWAYS, "glob_max_iter : 100,"), omniout_str(ALWAYS, "glob_max_minutes : 15,"), omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"), omniout_str(ALWAYS, "exact_soln_y1 (x) := ("), omniout_str(ALWAYS, "2.0 + sin(x) "), omniout_str(ALWAYS, ");"), omniout_str(ALWAYS, "exact_soln_y2 (x) := ("), omniout_str(ALWAYS, "2.0 - cos(x) "), omniout_str(ALWAYS, ");"), omniout_str(ALWAYS, "exact_soln_y2p (x) := ("), omniout_str(ALWAYS, "sin(x) "), omniout_str(ALWAYS, ");"), omniout_str(ALWAYS, "exact_soln_y2pp (x) := ("), omniout_str(ALWAYS, "cos(x) "), omniout_str(ALWAYS, ");"), omniout_str(ALWAYS, "exact_soln_y2ppp (x) := ("), omniout_str(ALWAYS, "-sin(x) "), omniout_str(ALWAYS, ");"), omniout_str(ALWAYS, "exact_soln_y2pppp (x) := ("), omniout_str(ALWAYS, "-cos(x) "), omniout_str(ALWAYS, ");"), omniout_str(ALWAYS, ""), omniout_str(ALWAYS, ""), omniout_str(ALWAYS, "/* END USER DEF BLOCK */"), omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"), glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false, glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64, glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0, glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30, glob_max_terms : max_terms, glob_html_log : true, array(array_type_pole, 1 + max_terms), array(array_1st_rel_error, 1 + max_terms), array(array_norms, 1 + max_terms), array(array_y1, 1 + max_terms), array(array_x, 1 + max_terms), array(array_y2, 1 + max_terms), array(array_tmp0, 1 + max_terms), array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms), array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms), array(array_m1, 1 + max_terms), array(array_y1_init, 1 + max_terms), array(array_last_rel_error, 1 + max_terms), array(array_y2_init, 1 + max_terms), array(array_pole, 1 + max_terms), array(array_y2_higher_work, 1 + 6, 1 + max_terms), array(array_y2_higher_work2, 1 + 6, 1 + max_terms), array(array_poles, 1 + 2, 1 + 3), array(array_y1_higher_work, 1 + 2, 1 + max_terms), array(array_y1_higher_work2, 1 + 2, 1 + max_terms), array(array_y1_set_initial, 1 + 3, 1 + max_terms), array(array_y2_set_initial, 1 + 3, 1 + max_terms), array(array_complex_pole, 1 + 2, 1 + 3), array(array_y2_higher, 1 + 6, 1 + max_terms), array(array_y1_higher, 1 + 2, 1 + max_terms), array(array_real_pole, 1 + 2, 1 + 3), term : 1, while term <= max_terms do (array_type_pole : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_1st_rel_error : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_norms : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_y1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_y2 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_y1_init : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_last_rel_error : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_y2_init : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_pole : 0.0, term : 1 + term), ord : 1, term while ord <= 6 do (term : 1, while term <= max_terms do (array_y2_higher_work : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 6 do (term : 1, while term <= max_terms do (array_y2_higher_work2 : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_poles : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y1_higher_work : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y1_higher_work2 : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 3 do (term : 1, while term <= max_terms do (array_y1_set_initial : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 3 do (term : 1, while term <= max_terms do (array_y2_set_initial : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_complex_pole : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 6 do (term : 1, while term <= max_terms do (array_y2_higher : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y1_higher : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_real_pole : 0.0, term : 1 + term), ord, term ord : 1 + ord), array(array_tmp4, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term), term array(array_tmp3, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term), term array(array_tmp2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term), term array(array_tmp1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term), term array(array_tmp0, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term), term array(array_y2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y2 : 0.0, term : 1 + term), term array(array_x, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term), term array(array_y1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y1 : 0.0, term : 1 + term), term array(array_const_0D0, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term), term array_const_0D0 : 0.0, array(array_const_5, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_5 : 0.0, term : 1 + term), term array_const_5 : 5, array(array_const_1, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term), term array_const_1 : 1, array(array_const_2D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_2D0 : 0.0, term : 1 + term), term array_const_2D0 : 2.0, array(array_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, x_start : 0.5, x_end : 10.0, 1 array_y1_init : exact_soln_y1(x_start), 1 + 0 array_y2_init : exact_soln_y2(x_start), 1 + 0 array_y2_init : exact_soln_y2p(x_start), 1 + 1 array_y2_init : exact_soln_y2pp(x_start), 1 + 2 array_y2_init : exact_soln_y2ppp(x_start), 1 + 3 array_y2_init : exact_soln_y2pppp(x_start), glob_h : 1.0E-5, 1 + 4 glob_look_poles : true, glob_max_iter : 10, glob_subiter_method : 3, glob_h : 1.0E-4, glob_look_poles : true, glob_max_iter : 100, glob_max_minutes : 15, glob_last_good_h : glob_h, glob_max_terms : max_terms, glob_max_sec : convfloat(3600.0) convfloat(glob_max_hours) + convfloat(60.0) convfloat(glob_max_minutes), glob_log10_abserr glob_log10_relerr glob_abserr : 10.0 , glob_relerr : 10.0 , chk_data(), array_y1_set_initial : true, array_y1_set_initial : false, 1, 1 1, 2 array_y1_set_initial : false, array_y1_set_initial : false, 1, 3 1, 4 array_y1_set_initial : false, array_y1_set_initial : false, 1, 5 1, 6 array_y1_set_initial : false, array_y1_set_initial : false, 1, 7 1, 8 array_y1_set_initial : false, array_y1_set_initial : false, 1, 9 1, 10 array_y1_set_initial : false, array_y1_set_initial : false, 1, 11 1, 12 array_y1_set_initial : false, array_y1_set_initial : false, 1, 13 1, 14 array_y1_set_initial : false, array_y1_set_initial : false, 1, 15 1, 16 array_y1_set_initial : false, array_y1_set_initial : false, 1, 17 1, 18 array_y1_set_initial : false, array_y1_set_initial : false, 1, 19 1, 20 array_y1_set_initial : false, array_y1_set_initial : false, 1, 21 1, 22 array_y1_set_initial : false, array_y1_set_initial : false, 1, 23 1, 24 array_y1_set_initial : false, array_y1_set_initial : false, 1, 25 1, 26 array_y1_set_initial : false, array_y1_set_initial : false, 1, 27 1, 28 array_y1_set_initial : false, array_y1_set_initial : false, 1, 29 1, 30 array_y2_set_initial : true, array_y2_set_initial : true, 2, 1 2, 2 array_y2_set_initial : true, array_y2_set_initial : true, 2, 3 2, 4 array_y2_set_initial : true, array_y2_set_initial : false, 2, 5 2, 6 array_y2_set_initial : false, array_y2_set_initial : false, 2, 7 2, 8 array_y2_set_initial : false, array_y2_set_initial : false, 2, 9 2, 10 array_y2_set_initial : false, array_y2_set_initial : false, 2, 11 2, 12 array_y2_set_initial : false, array_y2_set_initial : false, 2, 13 2, 14 array_y2_set_initial : false, array_y2_set_initial : false, 2, 15 2, 16 array_y2_set_initial : false, array_y2_set_initial : false, 2, 17 2, 18 array_y2_set_initial : false, array_y2_set_initial : false, 2, 19 2, 20 array_y2_set_initial : false, array_y2_set_initial : false, 2, 21 2, 22 array_y2_set_initial : false, array_y2_set_initial : false, 2, 23 2, 24 array_y2_set_initial : false, array_y2_set_initial : false, 2, 25 2, 26 array_y2_set_initial : false, array_y2_set_initial : false, 2, 27 2, 28 array_y2_set_initial : false, array_y2_set_initial : false, 2, 29 2, 30 if glob_html_log then html_log_file : openw("html/entry.html"), omniout_str(ALWAYS, "START of Soultion"), array_x : x_start, 1 array_x : glob_h, order_diff : 1, term_no : 1, 2 while term_no <= order_diff do (array_y1 : term_no term_no - 1 array_y1_init glob_h term_no --------------------------------------, term_no : 1 + term_no), factorial_1(term_no - 1) rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, term_no - 1 array_y1_init glob_h it array_y1_higher : ---------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), order_diff : 5, term_no : 1, while term_no <= order_diff do (array_y2 : term_no term_no - 1 array_y2_init glob_h term_no --------------------------------------, term_no : 1 + term_no), factorial_1(term_no - 1) rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, term_no - 1 array_y2_init glob_h it array_y2_higher : ---------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1, glob_clock_start_sec : elapsed_time_seconds(), start_array_y1(), if !array_y1_higher ! > glob_small_float ! 1, 1! then (tmp : !array_y1_higher !, log10norm : log10(tmp), ! 1, 1! if log10norm < glob_log10normmin then glob_log10normmin : log10norm), display_alot(current_iter), start_array_y2(), if !array_y2_higher ! > glob_small_float ! 1, 1! then (tmp : !array_y2_higher !, log10norm : log10(tmp), ! 1, 1! if log10norm < glob_log10normmin then glob_log10normmin : log10norm), display_alot(current_iter), glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL, " "), glob_reached_optimal_h : true, glob_optimal_clock_start_sec : elapsed_time_seconds(), while (glob_current_iter < glob_max_iter) and (array_x <= x_end) and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < 1 convfloat(glob_max_sec)) do (omniout_str (INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop"), glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 1 + glob_current_iter, if glob_subiter_method = 1 then atomall() elseif glob_subiter_method = 2 then (subiter : 1, while subiter <= 2 do (atomall(), subiter : 1 + subiter)) else (subiter : 1, while subiter <= glob_max_terms + 2 do (atomall(), subiter : 1 + subiter)), if glob_look_poles then check_for_pole(), array_x : glob_h + array_x , array_x : glob_h, order_diff : 1, ord : 2, 1 1 2 calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y1_higher_work : 2, iii array_y1_higher 2, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y1_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y1_higher_work2 : ----------------------------, ord : 1, ord, calc_term convfp(calc_term - 1)! calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (array_y1_higher_work : 1, iii array_y1_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y1_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y1_higher_work2 : ----------------------------, ord : 1, ord, calc_term convfp(calc_term - 1)! calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y1_higher_work : 1, iii array_y1_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y1_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y1_higher_work2 : ----------------------------, ord, calc_term convfp(calc_term - 1)! term_no : glob_max_terms, while term_no >= 1 do (array_y1 : array_y1_higher_work2 , ord : 1, term_no 1, term_no while ord <= order_diff do (array_y1_higher : ord, term_no array_y1_higher_work2 , ord : 1 + ord), term_no : term_no - 1), ord, term_no order_diff : 5, ord : 6, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 6, iii array_y2_higher 6, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 6, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 5, ord, calc_term convfp(calc_term - 1)! calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 5, iii array_y2_higher 5, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 5, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 5, ord, calc_term convfp(calc_term - 1)! calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 5, iii array_y2_higher 5, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 5, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 4, ord, calc_term convfp(calc_term - 1)! calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 4, iii array_y2_higher 4, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 4, calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 4, ord, calc_term convfp(calc_term - 1)! calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 4, iii array_y2_higher 4, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 4, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 4, ord, calc_term convfp(calc_term - 1)! calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 4, iii array_y2_higher 4, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 4, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 3, ord, calc_term convfp(calc_term - 1)! calc_term : 4, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 3, iii array_y2_higher 3, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 3, calc_term : 4, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 3, ord, calc_term convfp(calc_term - 1)! calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 3, iii array_y2_higher 3, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 3, calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 3, ord, calc_term convfp(calc_term - 1)! calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 3, iii array_y2_higher 3, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 3, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 3, ord, calc_term convfp(calc_term - 1)! calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 3, iii array_y2_higher 3, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 3, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 2, ord, calc_term convfp(calc_term - 1)! calc_term : 5, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 2, iii array_y2_higher 2, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 5, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 2, ord, calc_term convfp(calc_term - 1)! calc_term : 4, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 2, iii array_y2_higher 2, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 4, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 2, ord, calc_term convfp(calc_term - 1)! calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 2, iii array_y2_higher 2, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 2, ord, calc_term convfp(calc_term - 1)! calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 2, iii array_y2_higher 2, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 2, ord, calc_term convfp(calc_term - 1)! calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 2, iii array_y2_higher 2, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 1, ord, calc_term convfp(calc_term - 1)! calc_term : 6, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 1, iii array_y2_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 6, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 1, ord, calc_term convfp(calc_term - 1)! calc_term : 5, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 1, iii array_y2_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 5, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 1, ord, calc_term convfp(calc_term - 1)! calc_term : 4, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 1, iii array_y2_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 4, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 1, ord, calc_term convfp(calc_term - 1)! calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 1, iii array_y2_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 1, ord, calc_term convfp(calc_term - 1)! calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 1, iii array_y2_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 1, ord, calc_term convfp(calc_term - 1)! calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 1, iii array_y2_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord, calc_term convfp(calc_term - 1)! term_no : glob_max_terms, while term_no >= 1 do (array_y2 : array_y2_higher_work2 , ord : 1, term_no 1, term_no while ord <= order_diff do (array_y2_higher : ord, term_no array_y2_higher_work2 , ord : 1 + ord), term_no : term_no - 1), ord, term_no display_alot(current_iter)), omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!"), if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!"), glob_clock_sec : elapsed_time_seconds(), omniout_str(INFO, "diff(y1,x,1) = diff(y2,x,5);"), omniout_str(INFO, "diff(y2,x,1) = y1 - 2.0;"), omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "), prog_report(x_start, x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2012-06-13T03:46:11-05:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "mtest9"), logitem_str(html_log_file, "diff(y1,x,1) = diff(y2,x,5);"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_integer(html_log_file, glob_max_terms), logitem_float(html_log_file, array_1st_rel_error ), 1 logitem_float(html_log_file, array_last_rel_error ), 1 logitem_integer(html_log_file, glob_iter), logitem_pole(html_log_file, array_type_pole ), 1 if (array_type_pole = 1) or (array_type_pole = 2) 1 1 then (logitem_float(html_log_file, array_pole ), 1 logitem_float(html_log_file, array_pole ), 0) 2 else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0), logitem_time(html_log_file, convfloat(glob_clock_sec)), if glob_percent_done < 100.0 then (logitem_time(html_log_file, convfloat(glob_optimal_expect_sec)), 0) else (logitem_str(html_log_file, "Done"), 0), log_revs(html_log_file, " 090 "), logitem_str(html_log_file, "mtest9 diffeq.max"), logitem_str(html_log_file, "\ mtest9 maxima results"), logitem_str(html_log_file, "Test of revised logic - mostly affecting systems of eqs"), logend(html_log_file), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logitem_str(html_log_file, "diff(y2,x,1) = y1 - 2.0;"), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logitem_float(html_log_file, array_1st_rel_error ), 2 logitem_float(html_log_file, array_last_rel_error ), logditto(html_log_file), 2 logitem_pole(html_log_file, array_type_pole ), 2 if (array_type_pole = 1) or (array_type_pole = 2) 2 2 then (logitem_float(html_log_file, array_pole ), 1 logitem_float(html_log_file, array_pole ), 0) 2 else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0), logditto(html_log_file), if glob_percent_done < 100.0 then (logditto(html_log_file), 0) else (logditto(html_log_file), 0), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logend(html_log_file)), if glob_html_log then close(html_log_file)) (%o55) mainprog() := (define_variable(ALWAYS, 1, fixnum), define_variable(DEBUGL, 3, fixnum), define_variable(glob_iolevel, 5, fixnum), define_variable(glob_max_terms, 30, fixnum), define_variable(DEBUGMASSIVE, 4, fixnum), define_variable(INFO, 2, fixnum), define_variable(glob_no_eqs, 0, fixnum), define_variable(glob_max_hours, 0.0, float), define_variable(glob_look_poles, false, boolean), define_variable(glob_hmax, 1.0, float), define_variable(glob_initial_pass, true, boolean), define_variable(glob_clock_start_sec, 0.0, float), define_variable(centuries_in_millinium, 10.0, float), define_variable(days_in_year, 365.0, float), define_variable(glob_optimal_done, false, boolean), define_variable(glob_dump, false, boolean), define_variable(glob_optimal_expect_sec, 0.1, float), define_variable(glob_abserr, 1.0E-11, float), define_variable(glob_not_yet_start_msg, true, boolean), define_variable(glob_clock_sec, 0.0, float), define_variable(years_in_century, 100.0, float), define_variable(hours_in_day, 24.0, float), define_variable(glob_start, 0, fixnum), define_variable(glob_small_float, 1.0E-51, float), define_variable(glob_log10_relerr, 1.0E-11, float), define_variable(glob_hmin_init, 0.001, float), define_variable(glob_reached_optimal_h, false, boolean), define_variable(glob_html_log, true, boolean), define_variable(glob_max_minutes, 0.0, float), define_variable(glob_max_rel_trunc_err, 1.0E-11, float), define_variable(glob_large_float, 9.0E+100, float), define_variable(glob_almost_1, 0.999, float), define_variable(djd_debug, true, boolean), define_variable(glob_log10abserr, 0.0, float), define_variable(glob_orig_start_sec, 0.0, float), define_variable(glob_last_good_h, 0.1, float), define_variable(glob_disp_incr, 0.1, float), define_variable(min_in_hour, 60.0, float), define_variable(djd_debug2, true, boolean), define_variable(glob_log10relerr, 0.0, float), define_variable(glob_normmax, 0.0, float), define_variable(glob_iter, 0, fixnum), define_variable(glob_max_sec, 10000.0, float), define_variable(glob_warned2, false, boolean), define_variable(glob_max_iter, 1000, fixnum), define_variable(glob_log10_abserr, 1.0E-11, float), define_variable(glob_dump_analytic, false, boolean), define_variable(glob_h, 0.1, float), define_variable(glob_hmin, 1.0E-11, float), define_variable(glob_not_yet_finished, true, boolean), define_variable(sec_in_min, 60.0, float), define_variable(glob_display_flag, true, boolean), define_variable(glob_log10normmin, 0.1, float), define_variable(MAX_UNCHANGED, 10, fixnum), define_variable(glob_current_iter, 0, fixnum), define_variable(glob_unchanged_h_cnt, 0, fixnum), define_variable(glob_smallish_float, 1.0E-101, float), define_variable(glob_optimal_clock_start_sec, 0.0, float), define_variable(glob_relerr, 1.0E-11, float), define_variable(glob_subiter_method, 3, fixnum), define_variable(glob_curr_iter_when_opt, 0, fixnum), define_variable(glob_warned, false, boolean), define_variable(glob_optimal_start, 0.0, float), define_variable(glob_max_trunc_err, 1.0E-11, float), define_variable(glob_max_opt_iter, 10, fixnum), define_variable(glob_percent_done, 0.0, float), ALWAYS : 1, INFO : 2, DEBUGL : 3, DEBUGMASSIVE : 4, glob_iolevel : INFO, glob_orig_start_sec : elapsed_time_seconds(), MAX_UNCHANGED : 10, glob_curr_iter_when_opt : 0, glob_display_flag : true, glob_no_eqs : 2, glob_iter : - 1, opt_iter : - 1, glob_max_iter : 50000, glob_max_hours : 0.0, glob_max_minutes : 15.0, omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################"), omniout_str(ALWAYS, "##############temp/mtest9postode.ode#################"), omniout_str(ALWAYS, "diff(y1,x,1) = diff(y2,x,5);"), omniout_str(ALWAYS, "diff(y2,x,1) = y1 - 2.0;"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "Digits : 32,"), omniout_str(ALWAYS, "max_terms:30,"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* END FIRST INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "x_start : 0.5,"), omniout_str(ALWAYS, "x_end : 10.0,"), omniout_str(ALWAYS, "array_y1_init[0 + 1] : exact_soln_y1(x_start),"), omniout_str(ALWAYS, "array_y2_init[0 + 1] : exact_soln_y2(x_start),"), omniout_str(ALWAYS, "array_y2_init[1 + 1] : exact_soln_y2p(x_start),"), omniout_str(ALWAYS, "array_y2_init[2 + 1] : exact_soln_y2pp(x_start),"), omniout_str(ALWAYS, "array_y2_init[3 + 1] : exact_soln_y2ppp(x_start),"), omniout_str(ALWAYS, "array_y2_init[4 + 1] : exact_soln_y2pppp(x_start),"), omniout_str(ALWAYS, "glob_h : 0.00001 ,"), omniout_str(ALWAYS, "glob_look_poles : true,"), omniout_str(ALWAYS, "glob_max_iter : 10,"), omniout_str(ALWAYS, "glob_subiter_method : 3,"), omniout_str(ALWAYS, "/* END SECOND INPUT BLOCK */"), omniout_str(ALWAYS, "/* BEGIN OVERRIDE BLOCK */"), omniout_str(ALWAYS, "glob_h : 0.0001 ,"), omniout_str(ALWAYS, "glob_look_poles : true,"), omniout_str(ALWAYS, "glob_max_iter : 100,"), omniout_str(ALWAYS, "glob_max_minutes : 15,"), omniout_str(ALWAYS, "/* END OVERRIDE BLOCK */"), omniout_str(ALWAYS, "!"), omniout_str(ALWAYS, "/* BEGIN USER DEF BLOCK */"), omniout_str(ALWAYS, "exact_soln_y1 (x) := ("), omniout_str(ALWAYS, "2.0 + sin(x) "), omniout_str(ALWAYS, ");"), omniout_str(ALWAYS, "exact_soln_y2 (x) := ("), omniout_str(ALWAYS, "2.0 - cos(x) "), omniout_str(ALWAYS, ");"), omniout_str(ALWAYS, "exact_soln_y2p (x) := ("), omniout_str(ALWAYS, "sin(x) "), omniout_str(ALWAYS, ");"), omniout_str(ALWAYS, "exact_soln_y2pp (x) := ("), omniout_str(ALWAYS, "cos(x) "), omniout_str(ALWAYS, ");"), omniout_str(ALWAYS, "exact_soln_y2ppp (x) := ("), omniout_str(ALWAYS, "-sin(x) "), omniout_str(ALWAYS, ");"), omniout_str(ALWAYS, "exact_soln_y2pppp (x) := ("), omniout_str(ALWAYS, "-cos(x) "), omniout_str(ALWAYS, ");"), omniout_str(ALWAYS, ""), omniout_str(ALWAYS, ""), omniout_str(ALWAYS, "/* END USER DEF BLOCK */"), omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################"), glob_unchanged_h_cnt : 0, glob_warned : false, glob_warned2 : false, glob_small_float : 1.0E-200, glob_smallish_float : 1.0E-64, glob_large_float : 1.0E+100, glob_almost_1 : 0.99, glob_log10_abserr : - 8.0, glob_log10_relerr : - 8.0, glob_hmax : 0.01, Digits : 32, max_terms : 30, glob_max_terms : max_terms, glob_html_log : true, array(array_type_pole, 1 + max_terms), array(array_1st_rel_error, 1 + max_terms), array(array_norms, 1 + max_terms), array(array_y1, 1 + max_terms), array(array_x, 1 + max_terms), array(array_y2, 1 + max_terms), array(array_tmp0, 1 + max_terms), array(array_tmp1, 1 + max_terms), array(array_tmp2, 1 + max_terms), array(array_tmp3, 1 + max_terms), array(array_tmp4, 1 + max_terms), array(array_m1, 1 + max_terms), array(array_y1_init, 1 + max_terms), array(array_last_rel_error, 1 + max_terms), array(array_y2_init, 1 + max_terms), array(array_pole, 1 + max_terms), array(array_y2_higher_work, 1 + 6, 1 + max_terms), array(array_y2_higher_work2, 1 + 6, 1 + max_terms), array(array_poles, 1 + 2, 1 + 3), array(array_y1_higher_work, 1 + 2, 1 + max_terms), array(array_y1_higher_work2, 1 + 2, 1 + max_terms), array(array_y1_set_initial, 1 + 3, 1 + max_terms), array(array_y2_set_initial, 1 + 3, 1 + max_terms), array(array_complex_pole, 1 + 2, 1 + 3), array(array_y2_higher, 1 + 6, 1 + max_terms), array(array_y1_higher, 1 + 2, 1 + max_terms), array(array_real_pole, 1 + 2, 1 + 3), term : 1, while term <= max_terms do (array_type_pole : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_1st_rel_error : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_norms : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_y1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_x : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_y2 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp0 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp2 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp3 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_tmp4 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_y1_init : 0.0, term : 1 + term), term term : 1, while term <= max_terms do (array_last_rel_error : 0.0, term term : 1 + term), term : 1, while term <= max_terms do (array_y2_init : 0.0, term : 1 + term), term : 1, term while term <= max_terms do (array_pole : 0.0, term : 1 + term), ord : 1, term while ord <= 6 do (term : 1, while term <= max_terms do (array_y2_higher_work : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 6 do (term : 1, while term <= max_terms do (array_y2_higher_work2 : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_poles : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y1_higher_work : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y1_higher_work2 : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 3 do (term : 1, while term <= max_terms do (array_y1_set_initial : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 3 do (term : 1, while term <= max_terms do (array_y2_set_initial : 0.0, ord, term term : 1 + term), ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_complex_pole : 0.0, term : 1 + term), ord : 1 + ord), ord, term ord : 1, while ord <= 6 do (term : 1, while term <= max_terms do (array_y2_higher : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= max_terms do (array_y1_higher : 0.0, term : 1 + term), ord, term ord : 1 + ord), ord : 1, while ord <= 2 do (term : 1, while term <= 3 do (array_real_pole : 0.0, term : 1 + term), ord, term ord : 1 + ord), array(array_tmp4, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp4 : 0.0, term : 1 + term), term array(array_tmp3, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp3 : 0.0, term : 1 + term), term array(array_tmp2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp2 : 0.0, term : 1 + term), term array(array_tmp1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp1 : 0.0, term : 1 + term), term array(array_tmp0, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_tmp0 : 0.0, term : 1 + term), term array(array_y2, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y2 : 0.0, term : 1 + term), term array(array_x, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_x : 0.0, term : 1 + term), term array(array_y1, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_y1 : 0.0, term : 1 + term), term array(array_const_0D0, 1 + 1 + max_terms), term : 1, while term <= 1 + max_terms do (array_const_0D0 : 0.0, term : 1 + term), term array_const_0D0 : 0.0, array(array_const_5, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_5 : 0.0, term : 1 + term), term array_const_5 : 5, array(array_const_1, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_1 : 0.0, term : 1 + term), term array_const_1 : 1, array(array_const_2D0, 1 + 1 + max_terms), term : 1, 1 while term <= 1 + max_terms do (array_const_2D0 : 0.0, term : 1 + term), term array_const_2D0 : 2.0, array(array_m1, 1 + 1 + max_terms), term : 1, 1 while term <= max_terms do (array_m1 : 0.0, term : 1 + term), term array_m1 : - 1.0, x_start : 0.5, x_end : 10.0, 1 array_y1_init : exact_soln_y1(x_start), 1 + 0 array_y2_init : exact_soln_y2(x_start), 1 + 0 array_y2_init : exact_soln_y2p(x_start), 1 + 1 array_y2_init : exact_soln_y2pp(x_start), 1 + 2 array_y2_init : exact_soln_y2ppp(x_start), 1 + 3 array_y2_init : exact_soln_y2pppp(x_start), glob_h : 1.0E-5, 1 + 4 glob_look_poles : true, glob_max_iter : 10, glob_subiter_method : 3, glob_h : 1.0E-4, glob_look_poles : true, glob_max_iter : 100, glob_max_minutes : 15, glob_last_good_h : glob_h, glob_max_terms : max_terms, glob_max_sec : convfloat(3600.0) convfloat(glob_max_hours) + convfloat(60.0) convfloat(glob_max_minutes), glob_log10_abserr glob_log10_relerr glob_abserr : 10.0 , glob_relerr : 10.0 , chk_data(), array_y1_set_initial : true, array_y1_set_initial : false, 1, 1 1, 2 array_y1_set_initial : false, array_y1_set_initial : false, 1, 3 1, 4 array_y1_set_initial : false, array_y1_set_initial : false, 1, 5 1, 6 array_y1_set_initial : false, array_y1_set_initial : false, 1, 7 1, 8 array_y1_set_initial : false, array_y1_set_initial : false, 1, 9 1, 10 array_y1_set_initial : false, array_y1_set_initial : false, 1, 11 1, 12 array_y1_set_initial : false, array_y1_set_initial : false, 1, 13 1, 14 array_y1_set_initial : false, array_y1_set_initial : false, 1, 15 1, 16 array_y1_set_initial : false, array_y1_set_initial : false, 1, 17 1, 18 array_y1_set_initial : false, array_y1_set_initial : false, 1, 19 1, 20 array_y1_set_initial : false, array_y1_set_initial : false, 1, 21 1, 22 array_y1_set_initial : false, array_y1_set_initial : false, 1, 23 1, 24 array_y1_set_initial : false, array_y1_set_initial : false, 1, 25 1, 26 array_y1_set_initial : false, array_y1_set_initial : false, 1, 27 1, 28 array_y1_set_initial : false, array_y1_set_initial : false, 1, 29 1, 30 array_y2_set_initial : true, array_y2_set_initial : true, 2, 1 2, 2 array_y2_set_initial : true, array_y2_set_initial : true, 2, 3 2, 4 array_y2_set_initial : true, array_y2_set_initial : false, 2, 5 2, 6 array_y2_set_initial : false, array_y2_set_initial : false, 2, 7 2, 8 array_y2_set_initial : false, array_y2_set_initial : false, 2, 9 2, 10 array_y2_set_initial : false, array_y2_set_initial : false, 2, 11 2, 12 array_y2_set_initial : false, array_y2_set_initial : false, 2, 13 2, 14 array_y2_set_initial : false, array_y2_set_initial : false, 2, 15 2, 16 array_y2_set_initial : false, array_y2_set_initial : false, 2, 17 2, 18 array_y2_set_initial : false, array_y2_set_initial : false, 2, 19 2, 20 array_y2_set_initial : false, array_y2_set_initial : false, 2, 21 2, 22 array_y2_set_initial : false, array_y2_set_initial : false, 2, 23 2, 24 array_y2_set_initial : false, array_y2_set_initial : false, 2, 25 2, 26 array_y2_set_initial : false, array_y2_set_initial : false, 2, 27 2, 28 array_y2_set_initial : false, array_y2_set_initial : false, 2, 29 2, 30 if glob_html_log then html_log_file : openw("html/entry.html"), omniout_str(ALWAYS, "START of Soultion"), array_x : x_start, 1 array_x : glob_h, order_diff : 1, term_no : 1, 2 while term_no <= order_diff do (array_y1 : term_no term_no - 1 array_y1_init glob_h term_no --------------------------------------, term_no : 1 + term_no), factorial_1(term_no - 1) rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, term_no - 1 array_y1_init glob_h it array_y1_higher : ---------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), order_diff : 5, term_no : 1, while term_no <= order_diff do (array_y2 : term_no term_no - 1 array_y2_init glob_h term_no --------------------------------------, term_no : 1 + term_no), factorial_1(term_no - 1) rows : order_diff, r_order : 1, while r_order <= rows do (term_no : 1, while term_no <= 1 - r_order + rows do (it : - 1 + r_order + term_no, term_no - 1 array_y2_init glob_h it array_y2_higher : ---------------------------------, r_order, term_no factorial_1(term_no - 1) term_no : 1 + term_no), r_order : 1 + r_order), current_iter : 1, glob_clock_start_sec : elapsed_time_seconds(), start_array_y1(), if !array_y1_higher ! > glob_small_float ! 1, 1! then (tmp : !array_y1_higher !, log10norm : log10(tmp), ! 1, 1! if log10norm < glob_log10normmin then glob_log10normmin : log10norm), display_alot(current_iter), start_array_y2(), if !array_y2_higher ! > glob_small_float ! 1, 1! then (tmp : !array_y2_higher !, log10norm : log10(tmp), ! 1, 1! if log10norm < glob_log10normmin then glob_log10normmin : log10norm), display_alot(current_iter), glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 0, glob_iter : 0, omniout_str(DEBUGL, " "), glob_reached_optimal_h : true, glob_optimal_clock_start_sec : elapsed_time_seconds(), while (glob_current_iter < glob_max_iter) and (array_x <= x_end) and (convfloat(glob_clock_sec) - convfloat(glob_orig_start_sec) < 1 convfloat(glob_max_sec)) do (omniout_str (INFO, " "), omniout_str(INFO, "TOP MAIN SOLVE Loop"), glob_iter : 1 + glob_iter, glob_clock_sec : elapsed_time_seconds(), glob_current_iter : 1 + glob_current_iter, if glob_subiter_method = 1 then atomall() elseif glob_subiter_method = 2 then (subiter : 1, while subiter <= 2 do (atomall(), subiter : 1 + subiter)) else (subiter : 1, while subiter <= glob_max_terms + 2 do (atomall(), subiter : 1 + subiter)), if glob_look_poles then check_for_pole(), array_x : glob_h + array_x , array_x : glob_h, order_diff : 1, ord : 2, 1 1 2 calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y1_higher_work : 2, iii array_y1_higher 2, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y1_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y1_higher_work2 : ----------------------------, ord : 1, ord, calc_term convfp(calc_term - 1)! calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (array_y1_higher_work : 1, iii array_y1_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y1_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y1_higher_work2 : ----------------------------, ord : 1, ord, calc_term convfp(calc_term - 1)! calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y1_higher_work : 1, iii array_y1_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y1_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y1_higher_work2 : ----------------------------, ord, calc_term convfp(calc_term - 1)! term_no : glob_max_terms, while term_no >= 1 do (array_y1 : array_y1_higher_work2 , ord : 1, term_no 1, term_no while ord <= order_diff do (array_y1_higher : ord, term_no array_y1_higher_work2 , ord : 1 + ord), term_no : term_no - 1), ord, term_no order_diff : 5, ord : 6, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 6, iii array_y2_higher 6, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 6, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 5, ord, calc_term convfp(calc_term - 1)! calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 5, iii array_y2_higher 5, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 5, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 5, ord, calc_term convfp(calc_term - 1)! calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 5, iii array_y2_higher 5, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 5, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 4, ord, calc_term convfp(calc_term - 1)! calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 4, iii array_y2_higher 4, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 4, calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 4, ord, calc_term convfp(calc_term - 1)! calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 4, iii array_y2_higher 4, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 4, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 4, ord, calc_term convfp(calc_term - 1)! calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 4, iii array_y2_higher 4, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 4, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 3, ord, calc_term convfp(calc_term - 1)! calc_term : 4, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 3, iii array_y2_higher 3, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 3, calc_term : 4, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 3, ord, calc_term convfp(calc_term - 1)! calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 3, iii array_y2_higher 3, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 3, calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 3, ord, calc_term convfp(calc_term - 1)! calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 3, iii array_y2_higher 3, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 3, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 3, ord, calc_term convfp(calc_term - 1)! calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 3, iii array_y2_higher 3, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 3, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 2, ord, calc_term convfp(calc_term - 1)! calc_term : 5, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 2, iii array_y2_higher 2, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 5, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 2, ord, calc_term convfp(calc_term - 1)! calc_term : 4, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 2, iii array_y2_higher 2, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 4, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 2, ord, calc_term convfp(calc_term - 1)! calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 2, iii array_y2_higher 2, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 2, ord, calc_term convfp(calc_term - 1)! calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 2, iii array_y2_higher 2, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 2, ord, calc_term convfp(calc_term - 1)! calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 2, iii array_y2_higher 2, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 2, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 1, ord, calc_term convfp(calc_term - 1)! calc_term : 6, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 1, iii array_y2_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 6, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 1, ord, calc_term convfp(calc_term - 1)! calc_term : 5, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 1, iii array_y2_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 5, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 1, ord, calc_term convfp(calc_term - 1)! calc_term : 4, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 1, iii array_y2_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 4, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 1, ord, calc_term convfp(calc_term - 1)! calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 1, iii array_y2_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 3, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 1, ord, calc_term convfp(calc_term - 1)! calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 1, iii array_y2_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 2, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord : 1, ord, calc_term convfp(calc_term - 1)! calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (array_y2_higher_work : 1, iii array_y2_higher 1, iii --------------------- calc_term - 1 glob_h -------------------------------------, iii : iii - 1), temp_sum : 0.0, factorial_3(iii - calc_term, iii - 1) ord : 1, calc_term : 1, iii : glob_max_terms, while iii >= calc_term do (temp_sum : array_y2_higher_work + temp_sum, iii : iii - 1), ord, iii calc_term - 1 temp_sum glob_h array_y2_higher_work2 : ----------------------------, ord, calc_term convfp(calc_term - 1)! term_no : glob_max_terms, while term_no >= 1 do (array_y2 : array_y2_higher_work2 , ord : 1, term_no 1, term_no while ord <= order_diff do (array_y2_higher : ord, term_no array_y2_higher_work2 , ord : 1 + ord), term_no : term_no - 1), ord, term_no display_alot(current_iter)), omniout_str(ALWAYS, "Finished!"), if glob_iter >= glob_max_iter then omniout_str(ALWAYS, "Maximum Iterations Reached before Solution Completed!"), if elapsed_time_seconds() - convfloat(glob_orig_start_sec) >= convfloat(glob_max_sec) then omniout_str(ALWAYS, "Maximum Time Reached before Solution Completed!"), glob_clock_sec : elapsed_time_seconds(), omniout_str(INFO, "diff(y1,x,1) = diff(y2,x,5);"), omniout_str(INFO, "diff(y2,x,1) = y1 - 2.0;"), omniout_int(INFO, "Iterations ", 32, glob_iter, 4, " "), prog_report(x_start, x_end), if glob_html_log then (logstart(html_log_file), logitem_str(html_log_file, "2012-06-13T03:46:11-05:00"), logitem_str(html_log_file, "Maxima"), logitem_str(html_log_file, "mtest9"), logitem_str(html_log_file, "diff(y1,x,1) = diff(y2,x,5);"), logitem_float(html_log_file, x_start), logitem_float(html_log_file, x_end), logitem_float(html_log_file, array_x ), logitem_float(html_log_file, glob_h), 1 logitem_str(html_log_file, "16"), logitem_integer(html_log_file, glob_max_terms), logitem_float(html_log_file, array_1st_rel_error ), 1 logitem_float(html_log_file, array_last_rel_error ), 1 logitem_integer(html_log_file, glob_iter), logitem_pole(html_log_file, array_type_pole ), 1 if (array_type_pole = 1) or (array_type_pole = 2) 1 1 then (logitem_float(html_log_file, array_pole ), 1 logitem_float(html_log_file, array_pole ), 0) 2 else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0), logitem_time(html_log_file, convfloat(glob_clock_sec)), if glob_percent_done < 100.0 then (logitem_time(html_log_file, convfloat(glob_optimal_expect_sec)), 0) else (logitem_str(html_log_file, "Done"), 0), log_revs(html_log_file, " 090 "), logitem_str(html_log_file, "mtest9 diffeq.max"), logitem_str(html_log_file, "\ mtest9 maxima results"), logitem_str(html_log_file, "Test of revised logic - mostly affecting systems of eqs"), logend(html_log_file), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logitem_str(html_log_file, "diff(y2,x,1) = y1 - 2.0;"), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logitem_float(html_log_file, array_1st_rel_error ), 2 logitem_float(html_log_file, array_last_rel_error ), logditto(html_log_file), 2 logitem_pole(html_log_file, array_type_pole ), 2 if (array_type_pole = 1) or (array_type_pole = 2) 2 2 then (logitem_float(html_log_file, array_pole ), 1 logitem_float(html_log_file, array_pole ), 0) 2 else (logitem_str(html_log_file, "NA"), logitem_str(html_log_file, "NA"), 0), logditto(html_log_file), if glob_percent_done < 100.0 then (logditto(html_log_file), 0) else (logditto(html_log_file), 0), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logditto(html_log_file), logend(html_log_file)), if glob_html_log then close(html_log_file)) (%i56) mainprog() "##############ECHO OF PROBLEM#################" "##############temp/mtest9postode.ode#################" "diff(y1,x,1) = diff(y2,x,5);" "diff(y2,x,1) = y1 - 2.0;" "!" "/* BEGIN FIRST INPUT BLOCK */" "Digits : 32," "max_terms:30," "!" "/* END FIRST INPUT BLOCK */" "/* BEGIN SECOND INPUT BLOCK */" "x_start : 0.5," "x_end : 10.0," "array_y1_init[0 + 1] : exact_soln_y1(x_start)," "array_y2_init[0 + 1] : exact_soln_y2(x_start)," "array_y2_init[1 + 1] : exact_soln_y2p(x_start)," "array_y2_init[2 + 1] : exact_soln_y2pp(x_start)," "array_y2_init[3 + 1] : exact_soln_y2ppp(x_start)," "array_y2_init[4 + 1] : exact_soln_y2pppp(x_start)," "glob_h : 0.00001 ," "glob_look_poles : true," "glob_max_iter : 10," "glob_subiter_method : 3," "/* END SECOND INPUT BLOCK */" "/* BEGIN OVERRIDE BLOCK */" "glob_h : 0.0001 ," "glob_look_poles : true," "glob_max_iter : 100," "glob_max_minutes : 15," "/* END OVERRIDE BLOCK */" "!" "/* BEGIN USER DEF BLOCK */" "exact_soln_y1 (x) := (" "2.0 + sin(x) " ");" "exact_soln_y2 (x) := (" "2.0 - cos(x) " ");" "exact_soln_y2p (x) := (" "sin(x) " ");" "exact_soln_y2pp (x) := (" "cos(x) " ");" "exact_soln_y2ppp (x) := (" "-sin(x) " ");" "exact_soln_y2pppp (x) := (" "-cos(x) " ");" "" "" "/* END USER DEF BLOCK */" "#######END OF ECHO OF PROBLEM#################" "START of Soultion" x[1] = 0.5 " " y1[1] (analytic) = 2.479425538604203 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1224174381096272 " " y2[1] (numeric) = 1.1224174381096272 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " x[1] = 0.5 " " y1[1] (analytic) = 2.479425538604203 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1224174381096272 " " y2[1] (numeric) = 1.1224174381096272 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5001 " " y1[1] (analytic) = 2.479513294463118 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 8.77558589151838900000E-5 " " relative error = 3.539237281411125000E-3 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1224653850513207 " " y2[1] (numeric) = 1.1224653850513207 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5002 " " y1[1] (analytic) = 2.4796010455269 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 1.75506922697188370000E-4 " " relative error = 7.078030678112343000E-3 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.12251334076836 " " y2[1] (numeric) = 1.12251334076836 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5003 " " y1[1] (analytic) = 2.479688791794672 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 2.63253190468937250000E-4 " " relative error = 1.061638022239105600E-2 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.122561305260266 " " y2[1] (numeric) = 1.122561305260266 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5004 " " y1[1] (analytic) = 2.4797765332655555 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 3.50994661352466150000E-4 " " relative error = 1.415428594649414400E-2 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1226092785265591 " " y2[1] (numeric) = 1.1226092785265591 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5005 " " y1[1] (analytic) = 2.479864269938674 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 4.387313344711430000E-4 " " relative error = 1.769174788271749300E-2 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1226572605667593 " " y2[1] (numeric) = 1.1226572605667593 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5005999999999999 " " y1[1] (analytic) = 2.47995200181315 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 5.2646320894700340000E-4 " " relative error = 2.122876606329856500E-2 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.122705251380387 " " y2[1] (numeric) = 1.1227052513803868 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.977764018223156200000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5006999999999999 " " y1[1] (analytic) = 2.4800397288881055 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 6.1419028390252710000E-4 " " relative error = 2.476534052048801300E-2 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1227532509669618 " " y2[1] (numeric) = 1.1227532509669618 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5007999999999999 " " y1[1] (analytic) = 2.480127451162664 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 7.0191255846108190000E-4 " " relative error = 2.830147128656758700E-2 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1228012593260046 " " y2[1] (numeric) = 1.1228012593260044 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.977594904536536500000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5008999999999999 " " y1[1] (analytic) = 2.480215168635948 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 7.8963003174514770000E-4 " " relative error = 3.183715839377851400E-2 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1228492764570344 " " y2[1] (numeric) = 1.1228492764570344 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5009999999999999 " " y1[1] (analytic) = 2.48030288130708 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 8.7734270287720410000E-4 " " relative error = 3.537240187435731000E-2 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1228973023595716 " " y2[1] (numeric) = 1.1228973023595716 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5010999999999999 " " y1[1] (analytic) = 2.4803905891751836 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 9.650505709806190000E-4 " " relative error = 3.89072017605715860E-2 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1229453370331357 " " y2[1] (numeric) = 1.1229453370331357 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5011999999999999 " " y1[1] (analytic) = 2.4804782922393813 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 1.0527536351783162000E-3 " " relative error = 4.24415580846663200E-2 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1229933804772465 " " y2[1] (numeric) = 1.1229933804772465 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5012999999999999 " " y1[1] (analytic) = 2.480565990498796 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 1.1404518945927755000E-3 " " relative error = 4.59754708788638900E-2 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1230414326914233 " " y2[1] (numeric) = 1.1230414326914235 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.977171976575170800000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5013999999999998 " " y1[1] (analytic) = 2.480653683952551 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 1.2281453483478089000E-3 " " relative error = 4.950894017543564500E-2 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.123089493675186 " " y2[1] (numeric) = 1.123089493675186 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5014999999999998 " " y1[1] (analytic) = 2.4807413725997685 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 1.3158339955654520000E-3 " " relative error = 5.30419660065766400E-2 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1231375634280538 " " y2[1] (numeric) = 1.1231375634280538 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5015999999999998 " " y1[1] (analytic) = 2.4808290564395725 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 1.4035178353695166000E-3 " " relative error = 5.65745484045487700E-2 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1231856419495458 " " y2[1] (numeric) = 1.1231856419495458 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5016999999999998 " " y1[1] (analytic) = 2.4809167354710864 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 1.4911968668833708000E-3 " " relative error = 6.01066874015913500E-2 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1232337292391814 " " y2[1] (numeric) = 1.1232337292391814 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5017999999999998 " " y1[1] (analytic) = 2.4810044096934325 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 1.5788710892294944000E-3 " " relative error = 6.36383830299031600E-2 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1232818252964796 " " y2[1] (numeric) = 1.1232818252964798 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.976748843652168200000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5018999999999998 " " y1[1] (analytic) = 2.4810920791057347 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 1.6665405015316992000E-3 " " relative error = 6.71696353217319500E-2 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1233299301209596 " " y2[1] (numeric) = 1.1233299301209598 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.976664192514853100000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5019999999999998 " " y1[1] (analytic) = 2.4811797437071164 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 1.7542051029133532000E-3 " " relative error = 7.07004443093028700E-2 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1233780437121403 " " y2[1] (numeric) = 1.1233780437121406 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.976579533202351400000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5020999999999998 " " y1[1] (analytic) = 2.4812674034967 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 1.841864892496936000E-3 " " relative error = 7.42308100248005300E-2 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1234261660695406 " " y2[1] (numeric) = 1.1234261660695408 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.97649486571854220000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5021999999999998 " " y1[1] (analytic) = 2.48135505847361 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 1.929519869407148000E-3 " " relative error = 7.77607325004943100E-2 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1234742971926792 " " y2[1] (numeric) = 1.1234742971926794 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.976410190067303400000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5022999999999997 " " y1[1] (analytic) = 2.4814427086369695 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 2.0171700327664688000E-3 " " relative error = 8.1290211768559400E-2 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1235224370810748 " " y2[1] (numeric) = 1.123522437081075 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.976325506252513700000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5023999999999997 " " y1[1] (analytic) = 2.4815303539859017 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 2.1048153816987103000E-3 " " relative error = 8.48192478612199300E-2 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1235705857342462 " " y2[1] (numeric) = 1.1235705857342462 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5024999999999997 " " y1[1] (analytic) = 2.4816179945195302 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 2.1924559153272405000E-3 " " relative error = 8.83478408106774400E-2 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1236187431517117 " " y2[1] (numeric) = 1.1236187431517115 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.976156114147792400000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5025999999999997 " " y1[1] (analytic) = 2.481705630236979 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 2.2800916327758713000E-3 " " relative error = 9.1875990649146600E-2 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1236669093329894 " " y2[1] (numeric) = 1.1236669093329894 " " absolute error = 0.0 " " relative error = 0.0 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5026999999999997 " " y1[1] (analytic) = 2.4817932611373714 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 2.367722533168414900E-3 " " relative error = 9.54036974088373600E-2 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1237150842775985 " " y2[1] (numeric) = 1.1237150842775983 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.975986689435399700000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5027999999999997 " " y1[1] (analytic) = 2.4818808872198312 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 2.455348615628239000E-3 " " relative error = 9.89309611219371100E-2 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1237632679850564 " " y2[1] (numeric) = 1.1237632679850562 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.975901964861019000000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5028999999999997 " " y1[1] (analytic) = 2.4819685084834826 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 2.5429698792795996000E-3 " " relative error = 0.10245778182066419 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1238114604548817 " " y2[1] (numeric) = 1.1238114604548815 " " absolute error = 2.2204460492503130000000000000000E-16 " " relative error = 1.975817232146351300000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5029999999999997 " " y1[1] (analytic) = 2.4820561249274484 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 2.6305863232454210000E-3 " " relative error = 0.10598415953717863 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1238596616865926 " " y2[1] (numeric) = 1.123859661686592 " " absolute error = 6.6613381477509390000000000000000E-16 " " relative error = 5.92719747388581600000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5030999999999997 " " y1[1] (analytic) = 2.482143736550853 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 2.7181979466499584000E-3 " " relative error = 0.10951009430368938 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1239078716797066 " " y2[1] (numeric) = 1.1239078716797057 " " absolute error = 8.8817841970012520000000000000000E-16 " " relative error = 7.90259096924663200000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5031999999999996 " " y1[1] (analytic) = 2.4822313433528205 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 2.8058047486174686000E-3 " " relative error = 0.11303558615240063 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.123956090433742 " " y2[1] (numeric) = 1.123956090433741 " " absolute error = 1.1102230246251565000000000000000E-15 " " relative error = 9.87781492599692500000000000000E-14 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5032999999999996 " " y1[1] (analytic) = 2.4823189453324743 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 2.8934067282713194000E-3 " " relative error = 0.11656063511547607 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1240043179482164 " " y2[1] (numeric) = 1.124004317948215 " " absolute error = 1.3322676295501878000000000000000E-15 " " relative error = 1.1852869319773969000000000000E-13 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5033999999999996 " " y1[1] (analytic) = 2.4824065424889388 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 2.9810038847357667000E-3 " " relative error = 0.12008524122511048 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1240525542226476 " " y2[1] (numeric) = 1.124052554222646 " " absolute error = 1.5543122344752192000000000000000E-15 " " relative error = 1.3827754126230538000000000000E-13 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5034999999999996 " " y1[1] (analytic) = 2.4824941348213376 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 3.0685962171346226000E-3 " " relative error = 0.12360940451347596 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1241007992565533 " " y2[1] (numeric) = 1.1241007992565515 " " absolute error = 1.7763568394002505000000000000000E-15 " " relative error = 1.5802469321034910000000000000E-13 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5035999999999996 " " y1[1] (analytic) = 2.4825817223287956 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 3.1561837245925870000E-3 " " relative error = 0.12713312501277568 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1241490530494511 " " y2[1] (numeric) = 1.124149053049449 " " absolute error = 2.220446049250313000000000000000E-15 " " relative error = 1.97522387554120550000000000000E-13 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5036999999999996 " " y1[1] (analytic) = 2.482669305010436 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 3.2437664062330285000E-3 " " relative error = 0.13065640275515442 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1241973156008582 " " y2[1] (numeric) = 1.1241973156008558 " " absolute error = 2.4424906541753444000000000000000E-15 " " relative error = 2.17265298562813960000000000000E-13 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5037999999999996 " " y1[1] (analytic) = 2.482756882865383 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 3.3313442611802024000E-3 " " relative error = 0.134179237772788 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.124245586910292 " " y2[1] (numeric) = 1.1242455869102894 " " absolute error = 2.6645352591003757000000000000000E-15 " " relative error = 2.37006512644909240000000000000E-13 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5038999999999996 " " y1[1] (analytic) = 2.482844455892762 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 3.4189172885588090000E-3 " " relative error = 0.13770163009786537 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1242938669772704 " " y2[1] (numeric) = 1.124293866977267 " " absolute error = 3.3306690738754696000000000000000E-15 " " relative error = 2.9624541872047810000000000000E-13 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5039999999999996 " " y1[1] (analytic) = 2.482932024091696 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 3.506485487493105000E-3 " " relative error = 0.14122357976255287 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1243421558013098 " " y2[1] (numeric) = 1.124342155801306 " " absolute error = 3.774758283725532000000000000000E-15 " " relative error = 3.3573038814285960000000000000E-13 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5040999999999995 " " y1[1] (analytic) = 2.48301958746131 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 3.594048857106902000E-3 " " relative error = 0.14474508679899425 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1243904533819276 " " y2[1] (numeric) = 1.1243904533819233 " " absolute error = 4.218847493575595000000000000000E-15 " " relative error = 3.7521196314733890000000000000E-13 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5041999999999995 " " y1[1] (analytic) = 2.4831071460007275 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 3.6816073965244556000E-3 " " relative error = 0.14826615123934636 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.124438759718641 " " y2[1] (numeric) = 1.124438759718636 " " absolute error = 4.884981308350689000000000000000E-15 " " relative error = 4.3443729292763060000000000000E-13 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5042999999999995 " " y1[1] (analytic) = 2.4831946997090744 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 3.7691611048713547000E-3 " " relative error = 0.15178677311581493 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1244870748109668 " " y2[1] (numeric) = 1.1244870748109612 " " absolute error = 5.551115123125783000000000000000E-15 " " relative error = 4.9365753039526566000000000000E-13 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5043999999999995 " " y1[1] (analytic) = 2.4832822485854735 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 3.856709981270523000E-3 " " relative error = 0.1553069524604938 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1245353986584217 " " y2[1] (numeric) = 1.1245353986584155 " " absolute error = 6.217248937900877000000000000000E-15 " " relative error = 5.5287267482358460000000000000E-13 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5044999999999995 " " y1[1] (analytic) = 2.4833697926290506 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 3.944254024847549000E-3 " " relative error = 0.15882668930557922 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1245837312605227 " " y2[1] (numeric) = 1.1245837312605156 " " absolute error = 7.105427357601002000000000000000E-15 " " relative error = 6.3182732953434020000000000000E-13 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5045999999999995 " " y1[1] (analytic) = 2.4834573318389297 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 4.031793234726688000E-3 " " relative error = 0.16234598368320907 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1246320726167864 " " y2[1] (numeric) = 1.1246320726167784 " " absolute error = 7.993605777301127000000000000000E-15 " " relative error = 7.1077519234371990000000000000E-13 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5046999999999995 " " y1[1] (analytic) = 2.4835448662142356 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 4.1193276100326415000E-3 " " relative error = 0.16586483562553445 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1246804227267293 " " y2[1] (numeric) = 1.1246804227267204 " " absolute error = 8.881784197001252000000000000000E-15 " " relative error = 7.897162622843410000000000000E-13 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5047999999999995 " " y1[1] (analytic) = 2.4836323957540927 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 4.2068571498896645000E-3 " " relative error = 0.1693832451646838 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.124728781589868 " " y2[1] (numeric) = 1.1247287815898581 " " absolute error = 9.992007221626409000000000000000E-15 " " relative error = 8.883925960801090000000000000E-13 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5048999999999995 " " y1[1] (analytic) = 2.483719920457626 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 4.294381853422901700E-3 " " relative error = 0.17290121233281652 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.124777149205719 " " y2[1] (numeric) = 1.124777149205708 " " absolute error = 1.110223024625156500000000000000E-14 " " relative error = 9.8706043718007590000000000000E-13 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5049999999999994 " " y1[1] (analytic) = 2.4838074403239596 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 4.381901719756609000E-3 " " relative error = 0.17641873716205164 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1248255255737984 " " y2[1] (numeric) = 1.124825525573786 " " absolute error = 1.243449787580175300000000000000E-14 " " relative error = 1.105460144092893000000000000E-12 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5050999999999994 " " y1[1] (analytic) = 2.4838949553522194 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 4.469416748016375000E-3 " " relative error = 0.1799358196845569 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1248739106936225 " " y2[1] (numeric) = 1.1248739106936088 " " absolute error = 1.376676550535194000000000000000E-14 " " relative error = 1.2238496576796812000000000000E-12 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5051999999999994 " " y1[1] (analytic) = 2.483982465541529 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 4.556926937326011300E-3 " " relative error = 0.183452459932424 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1249223045647074 " " y2[1] (numeric) = 1.1249223045646923 " " absolute error = 1.50990331349021300000000000000E-14 " " relative error = 1.342228976493159000000000000E-12 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5052999999999994 " " y1[1] (analytic) = 2.4840699708910146 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 4.644432286811550600E-3 " " relative error = 0.18696865793782905 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1249707071865696 " " y2[1] (numeric) = 1.1249707071865527 " " absolute error = 1.68753899743023800000000000000E-14 " " relative error = 1.5000737233866213000000000000E-12 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5053999999999994 " " y1[1] (analytic) = 2.4841574713998003 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 4.731932795597249000E-3 " " relative error = 0.1904844137328721 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1250191185587244 " " y2[1] (numeric) = 1.125019118558706 " " absolute error = 1.8429702208777599000000000000E-14 " " relative error = 1.6381679124162896000000000000E-12 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5054999999999994 " " y1[1] (analytic) = 2.4842449670670113 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 4.819428462808250700E-3 " " relative error = 0.19399972734968407 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.125067538680688 " " y2[1] (numeric) = 1.125067538680668 " " absolute error = 2.02060590481778500000000000000E-14 " " relative error = 1.7959863166857085000000000000E-12 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5055999999999994 " " y1[1] (analytic) = 2.4843324578917723 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 4.906919287569256000E-3 " " relative error = 0.1975145988203734 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1251159675519764 " " y2[1] (numeric) = 1.1251159675519542 " " absolute error = 2.22044604925031300000000000000E-14 " " relative error = 1.9735263859791735000000000000E-12 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5056999999999994 " " y1[1] (analytic) = 2.484419943873209 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 4.994405269005852700E-3 " " relative error = 0.20102902817707938 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.125164405172105 " " y2[1] (numeric) = 1.1251644051720808 " " absolute error = 2.420286193682841300000000000000E-14 " " relative error = 2.15105115533106000000000000E-12 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5057999999999994 " " y1[1] (analytic) = 2.484507425010446 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 5.081886406243186000E-3 " " relative error = 0.20454301545191875 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1252128515405895 " " y2[1] (numeric) = 1.1252128515405633 " " absolute error = 2.620126338115369400000000000000E-14 " " relative error = 2.3285606225773312000000000000E-12 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5058999999999994 " " y1[1] (analytic) = 2.4845949013026094 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 5.169362698406399000E-3 " " relative error = 0.2080565606770035 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1252613066569457 " " y2[1] (numeric) = 1.125261306656917 " " absolute error = 2.86437540353290400000000000000E-14 " " relative error = 2.5455202152491285000000000000E-12 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5059999999999993 " " y1[1] (analytic) = 2.484682372748823 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 5.256834144620193000E-3 " " relative error = 0.21156966388442305 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1253097705206885 " " y2[1] (numeric) = 1.1253097705206574 " " absolute error = 3.10862446895043830000000000000E-14 " " relative error = 2.7624611021657236000000000000E-12 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5060999999999993 " " y1[1] (analytic) = 2.4847698393482136 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 5.344300744010599000E-3 " " relative error = 0.21508232510631556 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1253582431313336 " " y2[1] (numeric) = 1.1253582431313 " " absolute error = 3.35287353436797300000000000000E-14 " " relative error = 2.9793832806862725000000000000E-12 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5061999999999993 " " y1[1] (analytic) = 2.4848573010999058 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 5.431762495702763000E-3 " " relative error = 0.21859454437477877 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1254067244883965 " " y2[1] (numeric) = 1.12540672448836 " " absolute error = 3.641531520770513500000000000000E-14 " " relative error = 3.2357470783959750000000000000E-12 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5062999999999993 " " y1[1] (analytic) = 2.4849447580030244 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 5.5192193988213840000E-3 " " relative error = 0.22210632172188782 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.125455214591392 " " y2[1] (numeric) = 1.1254552145913526 " " absolute error = 3.95239396766555730000000000000E-14 " " relative error = 3.511818077186229000000000000E-12 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5063999999999993 " " y1[1] (analytic) = 2.485032210056696 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 5.6066714524929400000E-3 " " relative error = 0.22561765717978455 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1255037134398354 " " y2[1] (numeric) = 1.1255037134397927 " " absolute error = 4.26325641456060100000000000000E-14 " " relative error = 3.7878652585969425000000000000E-12 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5064999999999993 " " y1[1] (analytic) = 2.4851196572600447 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 5.6941186558416850000E-3 " " relative error = 0.22912855078051672 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1255522210332418 " " y2[1] (numeric) = 1.1255522210331954 " " absolute error = 4.640732242933154300000000000000E-14 " " relative error = 4.123071463244082000000000000E-12 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5065999999999993 " " y1[1] (analytic) = 2.4852070996121975 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 5.78156100799454000E-3 " " relative error = 0.23263900255623443 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1256007373711259 " " y2[1] (numeric) = 1.1256007373710757 " " absolute error = 5.018208071305708000000000000000E-14 " " relative error = 4.458248741934802000000000000E-12 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5066999999999993 " " y1[1] (analytic) = 2.485294537112279 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 5.868998508076206000E-3 " " relative error = 0.2361490125389939 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1256492624530026 " " y2[1] (numeric) = 1.1256492624529484 " " absolute error = 5.41788836017076400000000000000E-14 " " relative error = 4.8131230045530890000000000000E-12 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5067999999999993 " " y1[1] (analytic) = 2.4853819697594153 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 5.956431155212272000E-3 " " relative error = 0.23965858076088215 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1256977962783865 " " y2[1] (numeric) = 1.1256977962783283 " " absolute error = 5.8175686490358200000000000000E-14 " " relative error = 5.16796663213608000000000000E-12 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5068999999999992 " " y1[1] (analytic) = 2.485469397552732 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 6.043858948529213000E-3 " " relative error = 0.2431677072540172 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1257463388467925 " " y2[1] (numeric) = 1.12574633884673 " " absolute error = 6.26165785888588300000000000000E-14 " " relative error = 5.5622280462402260000000000000E-12 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5069999999999992 " " y1[1] (analytic) = 2.4855568204913547 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 6.131281887151729000E-3 " " relative error = 0.24667639205044098 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.125794890157735 " " y2[1] (numeric) = 1.125794890157668 " " absolute error = 6.70574706873594600000000000000E-14 " " relative error = 5.956455414179757000000000000E-12 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5070999999999992 " " y1[1] (analytic) = 2.4856442385744093 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 6.218699970206298000E-3 " " relative error = 0.2501846351822619 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1258434502107288 " " y2[1] (numeric) = 1.1258434502106567 " " absolute error = 7.21644966006351800000000000000E-14 " " relative error = 6.4098162659406910000000000000E-12 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5071999999999992 " " y1[1] (analytic) = 2.485731651801021 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 6.306113196818064000E-3 " " relative error = 0.25369243668153035 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1258920190052881 " " y2[1] (numeric) = 1.1258920190052106 " " absolute error = 7.74935671188359300000000000000E-14 " " relative error = 6.882859618038731000000000000E-12 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5072999999999992 " " y1[1] (analytic) = 2.4858190601703165 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 6.3935215661135030000E-3 " " relative error = 0.2571997965803452 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1259405965409273 " " y2[1] (numeric) = 1.1259405965408442 " " absolute error = 8.30446822419617100000000000000E-14 " " relative error = 7.375582912374639000000000000E-12 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5073999999999992 " " y1[1] (analytic) = 2.4859064636814217 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 6.480925077218647000E-3 " " relative error = 0.2607067149107828 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1259891828171602 " " y2[1] (numeric) = 1.1259891828170714 " " absolute error = 8.88178419700125200000000000000E-14 " " relative error = 7.887983590374765000000000000E-12 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5074999999999992 " " y1[1] (analytic) = 2.485993862333462 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 6.568323729259085000E-3 " " relative error = 0.26421319170489704 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1260377778335013 " " y2[1] (numeric) = 1.1260377778334065 " " absolute error = 9.48130463029883700000000000000E-14 " " relative error = 8.42005909299143000000000000E-12 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5075999999999992 " " y1[1] (analytic) = 2.4860812561255634 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 6.655717521360405000E-3 " " relative error = 0.26771922699473694 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1260863815894648 " " y2[1] (numeric) = 1.1260863815893636 " " absolute error = 1.01252339845814280000000000000E-13 " " relative error = 8.991525117540019000000000000E-12 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5076999999999992 " " y1[1] (analytic) = 2.4861686450568525 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 6.743106452649528000E-3 " " relative error = 0.27122482081240024 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1261349940845644 " " y2[1] (numeric) = 1.1261349940844563 " " absolute error = 1.08135722598490250000000000000E-13 " " relative error = 9.602376550459106000000000000E-12 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5077999999999991 " " y1[1] (analytic) = 2.4862560291264555 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 6.830490522252486000E-3 " " relative error = 0.27472997318994435 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1261836153183142 " " y2[1] (numeric) = 1.1261836153181988 " " absolute error = 1.15463194561016280000000000000E-13 " " relative error = 1.025260827723734600000000000E-11 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5078999999999991 " " y1[1] (analytic) = 2.486343408333498 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 6.917869729294868000E-3 " " relative error = 0.278234684159404 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1262322452902278 " " y2[1] (numeric) = 1.1262322452901048 " " absolute error = 1.23012711128467340000000000000E-13 " " relative error = 1.092249947938288800000000000E-11 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5079999999999991 " " y1[1] (analytic) = 2.486430782677106 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 7.0052440729031500000E-3 " " relative error = 0.2817389537528448 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1262808839998188 " " y2[1] (numeric) = 1.1262808839996878 " " absolute error = 1.31006316905768470000000000000E-13 " " relative error = 1.163176244637297200000000000E-11 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5080999999999991 " " y1[1] (analytic) = 2.4865181521564064 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 7.092613552203364000E-3 " " relative error = 0.28524278200230996 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.126329531446601 " " y2[1] (numeric) = 1.1263295314464616 " " absolute error = 1.39444011892919660000000000000E-13 " " relative error = 1.23803920610893300000000000E-11 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5081999999999991 " " y1[1] (analytic) = 2.4866055167705254 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 7.179978166322432000E-3 " " relative error = 0.2887461689398733 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1263781876300878 " " y2[1] (numeric) = 1.1263781876299397 " " absolute error = 1.48103751484995880000000000000E-13 " " relative error = 1.314867005695554100000000000E-11 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5082999999999991 " " y1[1] (analytic) = 2.4866928765185894 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 7.267337914386385000E-3 " " relative error = 0.29224911459756847 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.126426852549793 " " y2[1] (numeric) = 1.1264268525496355 " " absolute error = 1.5742962489184720000000000000E-13 " " relative error = 1.397601846364792000000000000E-11 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5083999999999991 " " y1[1] (analytic) = 2.4867802313997243 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 7.354692795521256000E-3 " " relative error = 0.29575161900742425 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1264755262052293 " " y2[1] (numeric) = 1.1264755262050623 " " absolute error = 1.66977542903623540000000000000E-13 " " relative error = 1.48230067160111900000000000E-11 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5084999999999991 " " y1[1] (analytic) = 2.486867581413057 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 7.442042808853966000E-3 " " relative error = 0.2992536822015003 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1265242085959106 " " y2[1] (numeric) = 1.1265242085957332 " " absolute error = 1.77413639335100020000000000000E-13 " " relative error = 1.574876402844700200000000E-11 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.508599999999999 " " y1[1] (analytic) = 2.486954926557714 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 7.529387953510991000E-3 " " relative error = 0.30275530421183366 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1265728997213498 " " y2[1] (numeric) = 1.1265728997211617 " " absolute error = 1.88071780371501520000000000000E-13 " " relative error = 1.669415094380663800000000000E-11 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.508699999999999 " " y1[1] (analytic) = 2.4870422668328214 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 7.6167282286183640000E-3 " " relative error = 0.30625648507043884 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1266215995810598 " " y2[1] (numeric) = 1.1266215995808606 " " absolute error = 1.99174010617753080000000000000E-13 " " relative error = 1.76788737844025880000000000E-11 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.508799999999999 " " y1[1] (analytic) = 2.4871296022375065 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 7.7040636333034480000E-3 " " relative error = 0.30975722480937906 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.126670308174554 " " y2[1] (numeric) = 1.126670308174343 " " absolute error = 2.10942374678779740000000000000E-13 " " relative error = 1.872263546383425600000000000E-11 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.508899999999999 " " y1[1] (analytic) = 2.4872169327708957 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 7.791394166692722000E-3 " " relative error = 0.3132575234606771 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.126719025501345 " " y2[1] (numeric) = 1.1267190255011217 " " absolute error = 2.2337687255458150000000000000E-13 " " relative error = 1.98254283010076700000000000E-11 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.508999999999999 " " y1[1] (analytic) = 2.4873042584321152 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 7.878719827912217000E-3 " " relative error = 0.31675738105633316 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1267677515609456 " " y2[1] (numeric) = 1.1267677515607095 " " absolute error = 2.3603341503530828000000000000E-13 " " relative error = 2.094783194747312000000000000E-11 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.509099999999999 " " y1[1] (analytic) = 2.4873915792202923 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 7.966040616089298000E-3 " " relative error = 0.32025679762839615 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.126816486352869 " " y2[1] (numeric) = 1.1268164863526193 " " absolute error = 2.4957813593573520000000000000E-13 " " relative error = 2.214896027511425400000000000E-11 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.509199999999999 " " y1[1] (analytic) = 2.4874788951345534 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 8.053356530350442000E-3 " " relative error = 0.3237557732088745 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1268652298766273 " " y2[1] (numeric) = 1.1268652298763637 " " absolute error = 2.63566946046012160000000000000E-13 " " relative error = 2.338939378534807300000000000E-11 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.509299999999999 " " y1[1] (analytic) = 2.487566206174026 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 8.140667569823012000E-3 " " relative error = 0.3272543078298076 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1269139821317333 " " y2[1] (numeric) = 1.126913982131455 " " absolute error = 2.78221889971064230000000000000E-13 " " relative error = 2.468883112487114400000000000E-11 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.509399999999999 " " y1[1] (analytic) = 2.487653512337836 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 8.227973733633043000E-3 " " relative error = 0.33075240152317653 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1269627431176996 " " y2[1] (numeric) = 1.126962743117406 " " absolute error = 2.9354296771089140000000000000E-13 " " relative error = 2.604726460599894300000000000E-11 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.509499999999999 " " y1[1] (analytic) = 2.4877408136251113 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 8.315275020908341000E-3 " " relative error = 0.33425005432102894 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1270115128340383 " " y2[1] (numeric) = 1.1270115128337288 " " absolute error = 3.09530179265493640000000000000E-13 " " relative error = 2.746468653963737300000000000E-11 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5095999999999989 " " y1[1] (analytic) = 2.4878281100349784 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 8.402571430775385000E-3 " " relative error = 0.33774726625535423 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1270602912802619 " " y2[1] (numeric) = 1.1270602912799357 " " absolute error = 3.261835246348710000000000000E-13 " " relative error = 2.894108923528388000000000000E-11 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5096999999999989 " " y1[1] (analytic) = 2.487915401566564 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 8.489862962361094000E-3 " " relative error = 0.34124403735815484 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1271090784558826 " " y2[1] (numeric) = 1.127109078455539 " " absolute error = 3.43503003819023430000000000000E-13 " " relative error = 3.047646500102863500000000000E-11 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5097999999999989 " " y1[1] (analytic) = 2.4880026882189963 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 8.577149614793278000E-3 " " relative error = 0.3447403676614641 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1271578743604125 " " y2[1] (numeric) = 1.127157874360051 " " absolute error = 3.61488616817950970000000000000E-13 " " relative error = 3.207080614355569700000000000E-11 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5098999999999989 " " y1[1] (analytic) = 2.4880899699914014 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 8.664431387198412000E-3 " " relative error = 0.34823625719725704 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.127206678993364 " " y2[1] (numeric) = 1.1272066789929833 " " absolute error = 3.80584452841503660000000000000E-13 " " relative error = 3.37635022870321600000000000E-11 "%" h = 1.0000E-4 " " " " "TOP MAIN SOLVE Loop" "NO POLE" "NO POLE" x[1] = 0.5099999999999989 " " y1[1] (analytic) = 2.4881772468829064 " " y1[1] (numeric) = 2.479425538604203 " " absolute error = 8.751708278703418000E-3 " " relative error = 0.35173170599752185 "%" h = 1.0000E-4 " " y2[1] (analytic) = 1.1272554923542482 " " y2[1] (numeric) = 1.127255492353848 " " absolute error = 4.0012437807490640000000000000E-13 " " relative error = 3.549544719797776400000000000E-11 "%" h = 1.0000E-4 " " "Finished!" "Maximum Iterations Reached before Solution Completed!" "diff(y1,x,1) = diff(y2,x,5);" "diff(y2,x,1) = y1 - 2.0;" Iterations = 100 "Total Elapsed Time "= 6 Minutes 12 Seconds "Elapsed Time(since restart) "= 6 Minutes 12 Seconds "Expected Time Remaining "= 4 Days 1 Hours 18 Minutes 22 Seconds "Optimized Time Remaining "= 4 Days 1 Hours 13 Minutes 44 Seconds "Time to Timeout "= 8 Minutes 47 Seconds Percent Done = 0.1063157894736725 "%" (%o56) true (%o56) diffeq.max